Tessellated data visualization system

ABSTRACT

A data visualization system and related methods may include generating a multi-dimensional graphical object, in which a tessellated arrangement of columns represents an underlying hierarchical data set. Parent-child relationships may be represented by adjacency of columns with respect to an X-Y plane. Magnitudes of underlying values and/or expressions may be represented by Z-axis heights of the columns.

CROSS-REFERENCES

This application is based upon and claims the benefit under 35 U.S.C.§119(e) of U.S. patent application Ser. No. 15/141,728 filed Apr. 28,2016, which claims priority to U.S. Provisional Patent Application Ser.No. 62/154,644 filed Apr. 29, 2015 and U.S. Provisional PatentApplication Ser. No. 62/209,276 filed Aug. 24, 2015, all of which areincorporated herein, in their entireties, for all purposes.

FIELD

This disclosure relates to systems and methods for the visualrepresentation and analysis of data. More specifically, the disclosedembodiments relate to three-dimensional visualization of hierarchicaldata.

INTRODUCTION

The volume and flow rate of contemporary “big data” is of a scale thatoutweighs the human mind's capacity of understanding. One focal point ofbig data tools is data analysis, to aid in data mining and the like.However, existing tools fail to adequately address a key component:comprehensive visual analysis.

Hierarchical data, in particular, presents challenges for visualanalysis. Hierarchical data is data which is organized into a tree-likestructure, where any single data element may be a “parent” to one ormore other data elements, each of which is a “child” to the parent.These child data elements may also be parents to one or more other dataelements in a multi-generational structure. That is, any one dataelement may have a parent, as well as any number of children.

Data is organized into hierarchical sets in many fields and for manypurposes; for example: company organizational structure, librarycollections, school course catalogs, patient information for hospitals,biological classifications, items in a department store, fileorganization structures in computers, election results, survey results,and budgeting, among many others.

Visualizing such hierarchical data sets requires methods capable ofshowing the parent-child relationships, the relative value of the dataelements, and potentially how the data elements change over time, amongother facets. No known method is capable of accurately conveying all ofthese aspects of a hierarchical data set, particularly in an intuitivesense that is easily understood by an untrained individual.

One known method of displaying hierarchical data is called a so-called“treemap.” Treemaps display hierarchical data in two dimensions as a setof nested rectangles, with each rectangle representing a data element.The area of each rectangle corresponds to the value of the associateddata element. Comparing the relative values of two data elements onopposing sides of a tree map may be difficult, as the relative size oftwo areas is often difficult to judge by eye, in particular when the twoareas are not next to one another. Parent-child relationships may beshown using divider lines. However, these divider lines are difficult tosee, particularly as one moves further down the generational ladder intothe data set. Moreover, when treemap data is displayed with a timedependence, the size of each rectangle may change, as well as therelative position of a rectangle within the treemap, thus making itdifficult to keep track of a particular data element over time.

Other known methods of displaying hierarchical data involve representingdata elements as circles arranged in a two-dimensional plane, with thearea of the circles representing the value of each data element, andsometimes including connecting lines to represent parent-childrelationships. Representing value in terms of area poses challenges forhumans, who can tell if one circle is larger than another but havedifficulty grasping how much bigger. Adding time dependence to the areaof the circles does not improve the ease with which they are understood.

SUMMARY

The present disclosure provides systems, apparatuses, and methodsrelating to the multi-dimensional visualization of hierarchical data. Insome examples, a method, implemented in a data processing system, mayinclude receiving, using a data processing system, one or more elementsof a data set; identifying, using a processor of the data processingsystem, a plurality of hierarchical data nodes of the data set, each ofthe data nodes having an associated quantitative value, and one or morerelationships between the data nodes, such that identifying the datanodes includes identifying a plurality of root nodes and one or moregenerations of child nodes; generating, using the data processingsystem, a multi-dimensional graphical object illustrating thequantitative values of the data nodes and the one or more relationshipsbetween the data nodes; wherein generating the graphical objectincludes: representing the plurality of root nodes as a circular,edge-to-edge cluster of columns, each such root node column having atessellatable cross-sectional shape; representing, adjacent to a firstroot node of the plurality of root nodes, one or more first child nodeshaving the first root node as a root, the one or more first child nodesrepresented as respective child node columns extending single file fromone unoccupied edge of the first root node; and

setting a respective height of each root node column and of each childnode column, such that the respective height corresponds to thequantitative value of the data node represented by the respectivecolumn; and transmitting the graphical object for display.

Features, functions, and advantages may be achieved independently invarious examples and embodiments of the present disclosure, or may becombined in yet other embodiments, further details of which can be seenwith reference to the following description and drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a table of illustrative hierarchical data.

FIG. 2 is an illustrative representation of relationships between nodesin a hierarchical data structure.

FIG. 3 is a schematic block diagram of a data visualization system inaccordance with aspects of the present disclosure.

FIG. 4 is an illustrative overhead plan view of a layout for atessellated column visualization topology in accordance with aspects ofthe present disclosure.

FIG. 5 is an illustrative data visualization (graphical object) usingthe tessellated column topology according to the present teachings.

FIG. 6 is an illustrative tessellated column visualization having adownward Z-offset feature.

FIG. 7 is an illustrative multipartite column representation of a datanode in accordance with aspects of the present disclosure.

FIG. 8 is another illustrative multipartite column representation of adata node in accordance with aspects of the present disclosure.

FIG. 9 is another illustrative multipartite column representation of adata node in accordance with aspects of the present disclosure.

FIG. 10 is an illustrative multi-level tessellated column visualization.

FIG. 11 is an illustrative example of data visualized using a staircasetopology according to the present teachings.

FIG. 12 is an illustrative example of data visualized using a stackedannular topology according to the present teachings.

FIG. 13 is a schematic diagram showing characteristics of anillustrative data flower or rose topology in accordance with aspects ofthe present disclosure.

FIG. 14 is an illustrative example of data visualized using a dataflower topology in accordance with aspects of the present disclosure.

FIG. 15 is an illustrative example of data visualized using a rosetopology in accordance with aspects of the present disclosure.

FIG. 16 is an illustrative example of data visualized using a reversehex index topology according to the present teachings.

FIG. 17 is an illustrative example of data visualized using a buildingtopology according to the present teachings.

FIG. 18 is an illustrative example of data visualized using a helixtopology according to the present teachings.

FIG. 19 is a flow chart depicting steps in an illustrative datavisualization method in accordance with aspects of the presentdisclosure.

FIG. 20 is a flow chart depicting steps in an illustrative method forvisualizing data using a tessellated column topology in accordance withaspects of the present disclosure.

FIG. 21 is a flow chart depicting steps in an illustrative method forvisualizing data using a rose topology in accordance with aspects of thepresent disclosure.

FIG. 22 is a schematic diagram of various components of an illustrativedata processing system.

FIG. 23 is a schematic representation of an illustrative distributeddata processing system.

DESCRIPTION

Various embodiments of a tessellated data visualization systemconfigured to represent hierarchical data in three dimensions aredescribed below and illustrated in the associated drawings. Unlessotherwise specified, the tessellated data visualization system and/orits various components may, but are not required to, contain at leastone of the structure, components, functionality, and/or variationsdescribed, illustrated, and/or incorporated herein. Furthermore, thestructures, components, functionalities, and/or variations described,illustrated, and/or incorporated herein in connection with the presentteachings may, but are not required to, be included in other datavisualization systems. The following description of various embodimentsis merely exemplary in nature and is in no way intended to limit thedisclosure, its application, or uses. Additionally, the advantagesprovided by the embodiments, as described below, are illustrative innature and not all embodiments provide the same advantages or the samedegree of advantages.

Definitions

The following definitions apply herein, unless otherwise indicated.

“Substantially” means to be essentially conforming to the particulardimension, range, shape, or other aspect modified by the term, such thata feature or component need not conform exactly. For example, a“substantially cylindrical” object means that the object resembles acylinder, but may have one or more deviations from a true cylinder.

“Comprising,” “including,” and “having” (and conjugations thereof) areused interchangeably to mean including but not necessarily limited to,and are open-ended terms not intended to exclude additional, unrecitedelements or method steps.

Terms such as “first”, “second”, and “third” are used to distinguish oridentify various members of a group, or the like, and are not intendedto show serial or numerical limitation.

Directional terms such as “up,” “down,” “vertical,” “horizontal,” andthe like should be understood in the context of the particularvisualization topology being used. For example, a tessellated columntopology may be created and oriented around defined X, Y, and Z axes. Inthose examples, the X-Y plane will define horizontal, with up beingdefined as the positive Z direction and down being defined as thenegative Z direction.

Overview

Hierarchical information or data, in general, includes records or nodesof data organized in a tree-like structure (i.e., a hierarchy), whereparent-child relationships are defined between the nodes and each set ofchild nodes combines in some meaningful way to produce their parent.Examples of hierarchical data include demographic data organized bycountry, state, county, municipality, etc.; business data organized bycorporate entity, division, department, expense category, etc.; andindividual health information, organized by health aspect, physiologicalsystem, organ, organ-related chemistry levels, etc. The traditional “orgchart” of a company is an example of hierarchical organization. Almostany system that can be described hierarchically can have data associatedwith each level of the hierarchy. This data may comprise activities,readings, or entries occurring over time, for example as transactions ina ledger or sensor data points entered in a log. These time-based datapoints, however, can be categorized and rolled up to generate the nodesin a selected hierarchical data organization rubric.

For any given parent node, one or more child nodes may exist. Eachparent node represents a combination of its respective child nodes. Forexample, the magnitude of a parent node may be equivalent to the sum ofthe magnitudes of its children. Each child will have no more than oneparent, but each parent may have multiple children. Nodes having zeroparents may be referred to as root nodes. Each level or layer ofchildren may be referred to as a “generation.”

FIG. 1 shows an illustrative example of hierarchical data, generallyindicated at 10. Hierarchical data 10 is represented in a table 12. Inthis tabular form, an index 14 is included to identify each data elementor node, as well as its relationship to other nodes. Three values 16,18, and 20 are listed for each data element, corresponding to threedifferent time periods T1, T2, and T3. Displaying data 10 in a table,such as table 12, may effectively communicate the values of the dataelements. However, determining parent-child relationships from such adata table is difficult and cannot be taken in visually without detailedinspection.

FIG. 2 shows that hierarchical data (e.g., data 10) may be representedas a forest 22 comprising tree structures 24, 26, and 28. A treestructure such as this may effectively represent the parent-childrelationships between data elements or nodes. However, the relativevalues (e.g., magnitudes) of the respective nodes are not easy todiscern from the 2-D tree layout, even if numerically indicated on thediagram.

Human minds intuitively categorize and organize informationhierarchically. To a great extent, our physiological brains arethemselves organized hierarchically (see, e.g., “On Intelligence,” byJeff Hawkins (2004), or “How to Create a Mind: the Secret of HumanThought Revealed” by Ray Kurzweil (2012)). Accordingly, databases allover the world are arranged with this type of organization. As dataflows into ever more affordable and ubiquitous memory stores, one ormore organizational rubrics must be imposed for humans to be able tounderstand and use the data. More often than not, this organization ishierarchical in nature.

Generally speaking, humans are more capable and efficient at intuitivelyprocessing visual representations of data rather than reviewing theunderlying data itself. However, existing methods and systems forvisualizing hierarchical data are less than adequate.

Existing solutions for visualizing hierarchical data typically have onething in common: the data is represented in a two-dimensional plane. Inaddition to the treemaps, circle maps, data tables, and tree structuresdescribed above, comb charts combine elements of two differenttwo-dimensional chart types into a single two-dimensional chart. This isnot a coincidence, as a prevailing view in the data visualizationcommunity is that three-dimensional representations of data can beinherently misleading. In other words, unless a person is intending torepresent a three-dimensional physical object, most visualizations ofdata are best left in two dimensions. However, in this case the dataitself is three- or even four-dimensional. As many data sets have morethan two dimensions, creating a two-dimensional representationnecessarily ignores one or more dimensions when creating thevisualization. Often, more than one 2-D visualization is required totell the whole story of the data set.

In the known visualization methods that do have 3-D capabilities, othershortcomings are present. In general, the spatial relationships betweendata points in these methods are not intuitive, and the problems oftwo-dimensional representations are not corrected. For example,representing data as connected spheres simply replaces the nonintuitiveand inaccurate judgment of circular area with the even less intuitiveand accurate judgment of spherical volume.

The various examples of tessellated data visualization systems describedherein, as well as related systems and methods, solve the technicalvisualization problems outlined above, in part by representing thehierarchical data as an inherently three-dimensional virtual objecthaving an intuitive, easily grasped arrangement. The hierarchical datamay be modeled as a three-dimensional object on a computing device. Themodel may be rotated, manipulated, and/or animated by a user.Surprisingly, and against the prevailing wisdom, such a model canaccurately, easily, and intuitively represent the entirety of a data setin a single visualization.

In general, as shown in FIG. 3, a data visualization system according tothe present teachings, generally indicated at 30, may include a dataprocessing module 32 coupled to a data store 34 (e.g., a database) ofhierarchical data. A mapping and visualization module 36 may be coupledto the data processing module, such that the mapping and visualizationmodule receives an output of the data processing module. An output ofdata processing module 32 may include a subset or modified subset 38 ofthe data in data store 34. Mapping and visualization module 36 may beconfigured to visually represent some or all of the hierarchical data(e.g., subset 38) in accordance with one or more selected topologies orvisual arrangements. The representation may be displayed, for exampleinteractively, on a graphical user interface (GUI) 40. Any or all of thecomponents shown in FIG. 3 may be local or remote (e.g., computers andstorage systems connected to a network), and/or may be located in the“cloud,” (e.g., software as a service—SaaS—provided over the Web).

More specifically, data store 34 may include any suitable data storeconfigured to store in memory the values and relationships between nodesand related data. For example, data store 34 may include data containedand organized in a relational database, such as a Microsoft Access orSQL database, one or more spreadsheets, such as Microsoft Excel orGoogle Sheets, JSON data objects, and/or other computer-readablefile(s), or any combination of these. The hierarchical data may bestored and correlated according to standard, well-known methods in theart. For example, the data may be in the form of an array, such as anonline analytical processing (OLAP) cube or hypercube, also referred toas a multidimensional dataset. Data in this form may be analyzed usingtypical operations, such as slicing, dicing, drilling down, drilling up,rolling up, and/or pivoting. When such a data store containsbusiness-related information, use of these sorts of analysis tools maybe referred to as Business Intelligence (BI).

Mapping and visualization module 36 may include any suitable softwareprogram or programs configured to produce three-dimensional (e.g.,having height, width, and depth) and/or four-dimensional (i.e.,time-based) renderings. These renderings may be referred to collectivelyherein as 3-D renderings. In some examples, 3-D renderings may beinteractive, such that a user can manipulate the view through the userinterface, e.g., by panning, rotating, zooming, selecting, and/or thelike, similar in function to known computer-aided design (CAD) systems.In some embodiments, some or all of these functions are carried outusing so-called geographic information systems (GIS) software formapping, and JavaScript/WebGL for rendering. In some examples, HTML5 maybe used for rendering on the Web.

GUI 40 may include any suitable user interface allowing the user to viewand interact with the 3-D rendering. In some examples, GUI 40 mayinclude any suitable mechanical or virtual user interface configured toallow an operator to communicate information to the software renderingprogram and/or to carry out one or more functions. For example, GUI 40may include one or more manipulable hardware or software controls, suchas a lever, dial, switch, slider, pushbutton, keypad/keyboard, mouse,touchpad, and/or knob, or the like, or any combination of these, any ofwhich may be implemented mechanically or virtually, such as on a screenor other display. Any manipulable control may be manipulated by a bodypart of the operator, such as by a hand, a foot, and/or one or morefingers or toes. In some examples, a user interface may include a voiceinterface capable of speech recognition, through which the operator mayprovide voice commands to the controller. In some examples, a userinterface may include a wearable computing device, such as an article ofclothing or a wrist- or head-mounted interface. In some examples, a userinterface may include any suitable device implanted on or in theoperator's body. In some examples, a user may interact with 3-Drenderings according to the present teachings via a virtual reality (VR)system (e.g., Oculus Rift, or the like), and/or an augmented realitysystem (e.g., Microsoft HoloLens, or the like).

Data visualizations may be rendered as static 3-D objects (e.g., on adisplay screen) that can be manipulated by the user, and/or as a seriesof visualizations (e.g., an animation) showing change over time (i.e.,4-D) or any other suitable categorization (e.g., change betweendepartments, from individual to individual, etc.). In some examples, auser may interact with the visualized 3-D object by moving within thesame virtual space as the object (e.g., using VR technology). In someexamples, a data visualization may be physically reproduced using a 3-Dprinter. For example, a user may wish to memorialize a meaningful dataset by generating a three-dimensional physical object for display on theuser's desk or display shelf.

The visual topologies and GUIs described herein are a significant andsubstantial improvement over existing data visualization topologies andGUIs. They solve the various problems described above, notably byproviding an interactive and intuitive interface for analyzing,comparing, tracking, and absorbing a spectrum or array of simple datasets and/or complex and deep data over time.

Data visualization systems in accordance with aspects of the presentdisclosure may be used for intuitive BI and other analyses. The databeing analyzed may represent any suitable operation, system, oractivity. For example, hierarchical data may represent accounting orother financial data for a company or individual, health-relatedinformation for a population or individual, climate information for oneor more geographical regions, cost or durational data related to one ormore work breakdown structures, etc.

Various embodiments of a tessellated data visualization system asdescribed herein may represent nodes (i.e., data elements) of ahierarchical data set as columns arranged in a pattern (e.g., atessellation) according to selected rules. The parent-childrelationships in the data set may be represented by the relativeproximity and/or arrangement of the columns. The height of the columnsmay be used to represent a value associated with each node. It may besimple and intuitive for a user to compare the relative heights of twocolumns in order to appreciate the relative value of the associatednodes in the underlying data set.

If the hierarchical data set has time-dependent data elements, a seriesof visualizations may be created for each data element, and thensequentially displayed so as to represent the passage of time as ananimation. In some examples, an animation of the change from a firstvalue to a second value may be presented seamlessly, e.g., as acontinuous morphing from one value to the next, and/or may provideadditional visual aspects to highlight the delta between the first andsecond values. As the relative position of each column is fixed by theparent-child relationships, the columns will not change position withinthe topology over time. However, the height of each column may change.Accordingly, a user may easily understand the underlying time-dependentbehavior of the data set by watching the columns move up and downrelative to one another over time. The user may manipulate the 3-Dvirtual object, e.g. by rotating it or zooming in or out on variouslocations. Thus, a user may gain a full appreciation for the underlyingdata set by viewing a representation of the entire data set frommultiple angles and vantage points.

As mentioned above, several interactive topologies may be used todisplay a selected portion (or all) of the data. Each of the followingvisualization topologies is described briefly here as an overview, anddescribed in further detail below along with other topologies andexamples.

A first topology may include mapping the data as a three-dimensionaltessellated spiral of geometric columns, also described as a tessellatedcolumn topology. See, e.g., FIGS. 4-5. This topology may be utilized torepresent a large amount of data several generations deep. Accordingly,it may be referred to as a main or overview topology, or the like. Someor all of the columns may have a hexagonal cross section. Accordingly,this topology may be referred to herein as a hex or tessellated hex. Inthis topology, magnitude of any given data point (e.g., value, absolutevalue, delta, etc.) may be represented by a positive or negative heightof a corresponding node. Change in value over time may be represented byanimating the visualization to vary the heights based on the time periodbeing represented. Such animation may be manually advanced or reversed,or played automatically, and may provide discrete, stepwise changes orcontinuous morphing animation, or any combination of these. As this isthe main (or overview) topology, the systems described herein may bereferred to generally as “tessellated data visualization systems.”Often, this topology will be a starting point in the overall analysis,because it can provide a sense of the overall unique structure andbehavior of the data set. Accordingly, in some examples, this may bereferred to as the FINGERPRINT™ topology.

Other topologies may be used to perform further analysis, to support themain topology, or independently as intuitive visualizations in their ownright. Many of these topologies may show, in a single visualization, thechange in one or more nodes or expressions over time. A topology fromthis general category of visualizations may be referred to as a“creature.” For example, a second topology may include mapping thetime-based magnitudes of a given node in a spiraling staircase orstair-stepped topology, with each node value being reflected as awedge-shaped column mapped in a cylindrical pattern. See FIG. 11. Thistopology may be referred to as a staircase or stair creature.

A third topology may include mapping a selected expression result ascoaxial rings (i.e., each ring being an annulus) on a three-dimensionalcylinder, where the radial size of each annulus represents the value ofthe expression for the corresponding time period. For example, anexpression may be a mathematical result based on the relationshipbetween a first parent node and a second parent node (e.g., totalrevenue minus cost of goods sold). See FIG. 12.

A fourth topology may include mapping a selected subset of data nodes(e.g., a set of grouped or allocated child data points) as rectangularor Bezier bars around the circumference of a three-dimensional cylinderwhose long axis represents time. One or more generations of nodes may bemapped in this fashion. This topology may be referred to as a starburst,rose, data flower, tree creature, and/or the like. See FIGS. 13-15.

A fifth topology may include mapping low-level data points, in time,either linearly side-by-side or as a spoke-to-hub topology. For example,transactional, time-based data points may be mapped along a line orspoke, either as actual value or cumulatively, culminating in acorresponding endpoint or central hub column showing the total for thattransaction group (e.g., account). This topology may be referred toherein as a reverse hex index (RHI) topology. See FIG. 16.

A sixth topology may include a modification of the tessellated topologydescribed herein, where the root (or other) nodes of a set ofhierarchical data are spaced from one another along a spiraling helix.The child data associated with each root node, as well as any subsequentgenerations, may remain in proximity to the root node according to thelayout rules. This helix topology may be used to avoid collisionsbetween lower generations of data associated with different root nodes,to show progression of a root node and the associated child data overtime, to illustrate sequential processing of data, and/or to showmultiple related hex creatures. See FIG. 18.

Aspects of a tessellated data visualization system may be embodied as acomputer method, computer system, or computer program product.Accordingly, aspects of the tessellated data visualization system maytake the form of an entirely hardware embodiment, an entirely softwareembodiment (including firmware, resident software, micro-code, and thelike), or an embodiment combining software and hardware aspects, all ofwhich may generally be referred to herein as a “circuit,” “module,” or“system.” Furthermore, aspects of the data visualization system may takethe form of a computer program product embodied in a non-transitorycomputer-readable medium (or media) having computer-readable programcode/instructions embodied thereon.

Any combination of computer-readable media may be utilized.Computer-readable media can be a computer-readable signal medium and/ora computer-readable storage medium. A computer-readable storage mediummay include an electronic, magnetic, optical, electromagnetic, infrared,and/or semiconductor system, apparatus, or device, or any suitablecombination of these. More specific examples of a computer-readablestorage medium may include the following: an electrical connectionhaving one or more wires, a portable computer diskette, a hard disk, arandom access memory (RAM), a read-only memory (ROM), an erasableprogrammable read-only memory (EPROM or Flash memory), an optical fiber,a portable compact disc read-only memory (CD-ROM), an optical storagedevice, a magnetic storage device, and/or any suitable combination ofthese and/or the like. In the context of this disclosure, acomputer-readable storage medium may include any suitable tangiblemedium that can contain or store a program for use by or in connectionwith an instruction execution system, apparatus, or device.

A computer-readable signal medium may include a propagated data signalwith computer-readable program code embodied therein, for example, inbaseband or as part of a carrier wave. Such a propagated signal may takeany of a variety of forms, including, but not limited to,electro-magnetic, optical, and/or any suitable combination thereof. Acomputer-readable signal medium may include any computer-readable mediumthat is not a computer-readable storage medium and that is capable ofcommunicating, propagating, or transporting a program for use by or inconnection with an instruction execution system, apparatus, or device.

Program code embodied on a computer-readable medium may be transmittedusing any appropriate medium, including but not limited to wireless,wireline, optical fiber cable, RF, and/or the like, and/or any suitablecombination of these.

Computer program code for carrying out operations for aspects of thedata visualization system may be written in one or any combination ofprogramming languages, including an object-oriented programming languagesuch as Java, Smalltalk, C++, and/or the like, and conventionalprocedural programming languages, such as the C programming language.More specifically, in some embodiments, computer program code may bewritten in Delphi using Embarcadero RAD Studio XE4. Graphics may begenerated using TatukGIS components. In some embodiments, computerprogram code may be developed in Embarcadero RAD Studio XE6, withgraphics generated using WebGL (e.g., Three.js and D3).

The program code may execute entirely on a user's computer, partly onthe user's computer, as a stand-alone software package, partly on theuser's computer and partly on a remote computer, or entirely on theremote computer or server. In the latter scenario, the remote computermay be connected to the user's computer through any type of network,including a local area network (LAN) or a wide area network (WAN),and/or the connection may be made to an external computer (for example,through the Internet using an Internet Service Provider).

Aspects of the data visualization systems are described below withreference to flowchart illustrations and/or block diagrams of methods,apparatuses, systems, and/or computer program products. Each blockand/or combination of blocks in a flowchart and/or block diagram may beimplemented by computer program instructions. The computer programinstructions may be provided to a processor of a general purposecomputer, special purpose computer, or other programmable dataprocessing apparatus to produce a machine, such that the instructions,which execute via the processor of the computer or other programmabledata processing apparatus, create means for implementing thefunctions/acts specified in the flowchart and/or block diagram block orblocks.

These computer program instructions can also be stored in acomputer-readable medium that can direct a computer, other programmabledata processing apparatus, and/or other device to function in aparticular manner, such that the instructions stored in thecomputer-readable medium produce an article of manufacture havinginstructions which implement the function/act specified in the flowchartand/or block diagram block or blocks.

The computer program instructions can also be loaded onto a computer,other programmable data processing apparatus, and/or other device tocause a series of operational steps to be performed on the device toproduce a computer-implemented process such that the instructions whichexecute on the computer or other programmable apparatus provideprocesses for implementing the functions/acts specified in the flowchartand/or block diagram block or blocks. See the discussion of “sequentialprocessing” below.

Any flowchart and/or block diagram in the drawings is intended toillustrate the architecture, functionality, and/or operation of possibleimplementations of systems, methods, and computer program productsaccording to aspects of the data visualization system. In this regard,each block may represent a module, segment, or portion of code, whichcomprises one or more executable instructions for implementing thespecified logical function(s). In some implementations, the functionsnoted in the block may occur out of the order noted in the drawings. Forexample, two blocks shown in succession may, in fact, be executedsubstantially concurrently, or the blocks may sometimes be executed inthe reverse order, depending upon the functionality involved. Each blockand/or combination of blocks may be implemented by special purposehardware-based systems (or combinations of special purpose hardware andcomputer instructions) that perform the specified functions or acts.With respect to the discussion of sequential processing (below), asubstantially similar description applies regarding each node orcombination of nodes.

EXAMPLES, COMPONENTS, AND ALTERNATIVES

The following sections describe selected aspects of exemplarytessellated data visualization systems as well as related systems and/ormethods. The examples in these sections are intended for illustrationand should not be interpreted as limiting the entire scope of thepresent disclosure. Each section may include one or more distinctinventions, and/or contextual or related information, function, and/orstructure.

Tessellated Column Topology

As shown in FIG. 4, this section describes various aspects of thethree-dimensional, tessellated column topology described briefly above.

With reference to FIG. 4, the layout of an illustrative spiraltessellation topology will now be described. FIG. 4 is an overhead planview of a tessellated column topology 100, showing the geometricarrangement of the topology in an X-Y plane. Note that the X, Y, and Zaxes are indicated in FIG. 4 for reference purposes. In general, thetopologies described in this section are configured to provide anintuitive model of hierarchical data in terms of Z-height columns thatare tessellatable with respect to the X-Y plane. In this example, eachof the columns is hexagonal. Each column (or the grid location where acolumn is disposed) may interchangeably be referred to as a node. Itshould be understood, and is shown in later figures, that the value ormagnitude of each node is expressed as an orthogonal height (or depth)of the respective geometric column (i.e., in the Z axis).

FIG. 4 shows an arrangement of six root nodes 102, 104, 106, 108, 110,and 112, having respective indices 1-6, disposed in a contiguouscircular formation, edge-to-edge, around an imaginary center point 114.Each root node represents a first-generation parent in the underlyinghierarchical data set (or subset). Although a small gap is shown betweennode edges in FIG. 4, it should be understood that the nodes may shareedges in the visualization. The six root nodes may be arranged in anyorder, such as in a configurable order or selected order (e.g.,alphabetically, by magnitude, by underlying index value, etc.). To aidin understanding the layout and relationships between the nodes, FIG. 4includes node labels reflecting illustrative index values.

Child data nodes are shown in relation to their respective parent nodes.For example, child nodes 116 (index 1.1), 118 (1.2), and 120 (1.3) areall children of root node 102 (1). As shown in FIG. 4, these child nodesare disposed radially with respect to node 102 and center point 114, ina single-file, edge-to-edge adjacency. Although nodes 116, 118, and 120are shown laid out in order of their respective index values, anysuitable order may be used. For example, child nodes 116, 118, and 120may be arranged in order of descending magnitude.

In this example, child node 116 (1.1) has its own children. Accordinglychild node 116 is a parent node with respect to child nodes 122 (1.1.1)and 124 (1.1.2). As mentioned above, each subsequent set of children maybe referred to as a generation. To indicate the relationship betweenchild nodes 122 and 124, those nodes are disposed radially with respectto node 116, again in a single-file, edge-to-edge adjacency. Anoriginating edge of the parent node may be chosen such that the childrenextend in a clockwise (CW) or counterclockwise (CCW) direction from therespective parent. A consistent rule for this CW or CCW extension shouldbe followed throughout any given topology/visualization. In the exampleof FIG. 4, the second generation extends radially from the firstgeneration root nodes, and all children of subsequent generations extendCW from their parents.

Accordingly, child nodes 126 (2.1), 128 (2.2), 130 (2.3), and 132 (2.4)extend radially from root node 104 (2), and node 126 (2.1) is the parentof child nodes 134 (2.1.1), and 136 (2.1.2), which extend in a CWdirection from their parent. Similarly, node 128 (2.2) is a parent ofchild nodes 138 (2.2.1), 140 (2.2.2), and 142 (2.2.3), which extend in aCW direction from their parent. Moving to the next generation, a node144 (2.1.2.1) is the child of node 136 (2.1.2), and a node 146 (2.2.3.1)is the child of node 142 (2.2.3). These nodes, and any other children oftheir generation, are arranged in a fashion similar to the previousgenerations. Specifically, they protrude from one edge of the parent insingle-file, edge-to-edge alignment, again in a CW direction when viewedfrom above (i.e., normal to the X-Y plane).

Although four generations of hierarchical data are discussed in thisexample, more or fewer may be displayed. In many cases, displayinggreater than three generations (root nodes, their children, andgrandchildren) can result in collisions between adjacent nodes. Forexample, it can be seen in FIG. 4 that a hypothetical third generationnode at 2.1.4 would overlap with fourth generation node 2.2.3.1 (i.e.,node 146). This situation may be addressed by analyzing no more thanthree generations in any given visualization, and/or by various othermethods, as described below with respect to FIGS. 6, 8, and 18.

Although six root nodes are shown in FIG. 4, more or fewer may bevisualized. In some examples, six node positions are available, butfewer than six are occupied. In other words, fewer than six root nodes(i.e., parent categories of data) may be displayed in a six-root-nodehexagonal visualization (see, e.g., FIG. 18). In some examples, thenumber of root node positions may correspond exactly with the number ofroot nodes of data. For example, three triangular root nodes may form acomplete contiguous circle around center 114 (or four square root nodes,eight octagonal root nodes, etc.).

Returning to the present example, additional child nodes 148 (3.1), 150(4.1), 152 (5.1), and 154 (6.1) are shown (in phantom lines) withrespect to the remaining root nodes (106, 108, 110, and 112), indicatingthat similar arrangements may be present for any or all of those nodesas well. As described above and shown in FIG. 4, the one or morechildren for any given parent node extend or protrude from one edge ofthe parent node in single file alignment.

This consistent mapping of a repeated pattern sets up a spiraling visualflow centered on the root nodes. When considered from the child or leafnodes toward their respective parents, as indicated by the dashed arrowsin FIG. 4, this flow reflects the actual flow of data as each generationis rolled up into the parent nodes. Accordingly, the layout of thevisual topology graphically represents the data in an intuitive andmeaningful way. A path can be identified from any leaf node, progressinghierarchically to the root node. This forms part of the intuitive natureof the data representation. An observer can easily determine whichchildren resulted in the value observed at the parent node, as well ascompare each child to the others in that generation to determinerelative contributions.

Additional and/or clarifying information can be communicated viacolor-coding of the various nodes. For example, each set of child nodesmay share a common color scheme, allowing visual separation andgrouping. Moreover, each node may include corresponding indicia, whichmay be selected to show a category name, an index value, date-relatedinformation, magnitude, and/or the like, or any combination of these.

Although hexagonal columns are shown in FIG. 3 and elsewhere, anysuitable tessellatable column shape(s) may be utilized. These shapes maybe used independently or together with the hex geometry, as best suitedto the data at hand. In terms of column shape, root nodes may be thesame as or different than child nodes. For example, three root nodes maybe represented by columns having a triangular cross section. In otherexamples, six central root nodes may be arranged as shown in FIG. 4,with child nodes represented as columns having a square cross section.In still other examples, eight central root nodes may be present, eachwith an octagonal cross section. Any suitable combination oftessellating cross-sectional shapes may be utilized.

In general, columns having a tessellatable cross section may themselvesbe tessellated, at least in terms of a two-dimensional “floor plan.” Thefaces or facets of neighboring columns (corresponding to the edges ofthe tessellatable shapes) can be placed immediately adjacent to eachother similar to what is shown in FIGS. 4 and 5. In some examples, thecolumns may have non-tessellatable cross sections, but may nonethelessbe mapped onto a tessellated grid similar to the one described abovewith respect to FIG. 4. For example, cylindrical (round) columns may bemapped onto the same “floor plan” as if they were hexagonal columns,without straying from the scope of the present disclosure. In someexamples, tessellatable column shapes may be arranged as if they were adifferent shape. For example, square cross-section columns may berepresented within a hexagonal or octagonal (etc.) topology, withchildren extending from a parent node, for example, as if from anunoccupied edge of an imaginary hexagon shape.

Any visualization of data using a spiral tessellation topology can beshown as a static snapshot, i.e., having the values or magnitudesassociated with a single time period (e.g., one column of data in FIG.2). Additionally or alternatively, the data visualization system may beconfigured to load or map the data for a plurality of periods (e.g., allcolumns of FIG. 2) as a plurality of static visualizations. Each periodmay comprise a frame of an animation, such that the sequence ofvisualizations may be displayed as an animated series, sometimesreferred to as a flipbook. The animation may be discrete or continuous,user-controlled or automatic, or any combination of these.

As will be clear after reviewing the following examples, the magnitudeof the underlying (i.e., associated) data for each node is representedvisually by the Z-axis height of the column at that node. As mentionedabove, height may be positive and extend above the X-Y plane (i.e., “up”with respect to the X-Y plane) for magnitudes greater than zero.Likewise, height may be negative and extend below the X-Y plane (i.e.,“down” with respect to the X-Y plane) for magnitudes less than zero. Ofcourse, in some examples, the 3D visualization may be manipulated (e.g.,spun, flipped, or rotated). Accordingly, up and down are relative termscorresponding to the positive and negative Z axis, respectively.

Illustrative Visualization Using Tessellated Column Topology

As shown in FIG. 5, this section describes various aspects of anillustrative tessellated column visualization 200. Visualization 200 isan example of tessellated column topology 100, described above, usinghexagonal columns (also referred to herein as a “hex topology”).Accordingly, similar and/or related components may be labeled withsimilar reference numbers.

FIG. 5 is a perspective view of data visualization 200. Althoughvisualization 200 is shown in perspective, it may be shown in anisometric or orthographic manner, for example, to allow more directvisual comparison of elements distant from each other within thetopology. As mentioned above, values or magnitudes of each of the nodesare shown as a height on the Z axis.

Visualization 200 shows three generations of hierarchical data, laid outaccording to the rules described above. Third generation child nodes 202extend CW from (or lead CCW into) their parents, second generation childnodes 204. Nodes 204 extend radially from (or lead radially into) theirrespective parents, which are central root nodes 206, 208, 210, 212,214, and 216. Six spiral arms 218, 220, 222, 224, 226, and 228 extendfrom (or flow into) the central root nodes, such that each spiral arm iscoupled to a single respective root node.

Spiral arm 218 is labeled in greater detail in FIG. 5 for illustrativepurposes, to show indices and values for each node. For example,informational indicia 230 on column nodes 232 of arm 218 shows that thevalues of child nodes 1.5.1 (value=60), 1.5.2 (value=13), and 1.5.3(value=86) flow into and result in (in this case, add up to) theirparent node 1.5 (value=159). Each of the other arms is organized insimilar fashion.

FIG. 5 includes arrows on spiral arm 222 to show the flow of informationfor each generation. Specifically, arrows 234, 236, 238, 240, and 242indicate each of the third generation groups of child nodes flowing intoa respective parent. These parents are themselves second generationchild nodes, and arrow 244 indicates how the second generation nodesflow into their respective root node 210.

Z-Angle

FIG. 6 shows a tessellated column visualization 300 having an additionalfeature. Visualization 300 includes a plurality of spiral arms 302. Inthis example, the spiral arms of the topology are each angled downwardapproximately 35 degrees in the −Z direction (also referred to as theZ-angle and/or Z-offset). In other words, as one moves outward from thecenter, each node in any given generation within a spiral arm isdisposed farther below the X-Y plane as compared to the immediatelyprevious node.

This is an optional and variable feature, selectable by the user tofacilitate analysis. For example, angling of the spiral arms may beuseful when one or more generations of children would otherwise crossover or interfere with one or more other nodes as described above. Withthe angled feature, such a circumstance would result in the series ofchildren passing under or over the others, thereby avoiding visualambiguity and collision. Any suitable angle may be selected, positive ornegative with respect to the Z axis. In some examples, different spiralarms may be displayed at different Z-angles. For example, successivelyadjacent arms may alternate between a positive Z-angle and a negativeZ-angle, or between a flat (zero) angle and a positive or negativeangle.

Alternative Column Sub-Topologies

Turning to FIGS. 7-10, alternative embodiments are partially depicted,wherein some or all of the node columns of the hex visualization may bemultipartite in nature. In some examples, a column may be divided intosub-parts, such as multiple smaller subcolumns that together form thetessellatable shape. Each subcolumn could have an independentlymeaningful Z-height. For example, as shown in FIG. 7, a hexagonal node320 may include two or more concentric, tubular columns, shown here assubcolumn 322 and subcolumn 324. In another example, as shown in FIG. 8,a hexagonal node 326 may include three subcolumns 328, 330, and 332,each of which has a diamond or parallelogram cross section. Eachsubcolumn may have a Z-height corresponding to an aspect of the overallnode.

In some examples, a full column may have adjacent side-members, whichthemselves have meaningful Z-heights. For example, as shown in FIG. 9, anode 334 may be hexagonal, and each side of the hexagon may include arespective rectangular side member 336. These side members may be anysuitable shape and size, and may be configured to have a height in the Zdirection. The general layout of the hex topology will remain intact,with side members being disposed interstitially between columns. Forexample, a second, adjacent column node 334′ having side members 336′ isshown in FIG. 9 to illustrate this point.

Each of the multiple side members or subcolumns may represent adifferent item or aggregation, and together may “add up” or otherwisecorrespond to the item represented by the node overall. For example, hexnode 334 may represent revenue, and side members 336 may represent thecash, adjustments, and accrued amounts for debits and credits (totalingsix pieces of information) that go into that revenue amount. Any othersuitable components may be represented. For example, twelve side membersmay be present. In those examples, a central node that represents annualsales may have twelve corresponding side members that represent monthlysales. In this manner, a significant amount of added information can berepresented in the hex visualization without diverting from the generaltopology, which still shows the original parent-child organization.

In some examples, such added information may be shown separated from themain topology, but in recognizable relation to it. For example, FIG. 10depicts a tessellated hex visualization 340. In this example, amulti-level representation is utilized to show drill-down orsecondary-detail information relating to each of the hex nodes. Forexample, data 342 for the accounts that comprise each rolled up hex nodecan be shown in a vertically aligned representation, below therespective hex node.

Supporting Topologies

Drill Down:

This section describes various aspects of the supporting topologies,described briefly above, which facilitate a user “drilling down” intothe data. Drilling down may allow a user to gain more detailedinformation about a data set, see how data evolves over time, see howrelationships between data elements evolve over time, and/or any otherappropriate analysis of the underlying data; see FIGS. 11-18.

In some examples described herein, the values represented in thesupporting topologies may be values of data elements themselves. In someexamples, the values represented may include one or more outputs of oneor more expressions which have the underlying data elements as inputs.Expressions may include, for example, mathematical operations on thevalues of one or more data elements, mathematical combinations of datanodes, and/or the like. In some examples, the values represented mayinclude values both of data elements and of expressions. In someexamples, the values represented may vary over time.

FIG. 11 depicts various aspects of a staircase topology, generallyindicated at 400. The staircase topology may be used to show how asingle data element or node evolves over time. In this topology, time isdepicted as flowing in an axial direction. In other words, timeprogresses generally in a direction shown vertically upward in FIG. 11,as indicated by arrow 402. Each “step” or wedge in the spiral staircasemay correspond to a value of a particular data element during a timeperiod. The height or size of each step reflects the corresponding valueof the underlying data element.

Staircase topology 400 includes a plurality of steps 404 arranged in aspiraling staircase around a central axis 406. The plurality of stepsmay include a first step 408 corresponding to a first time interval anda second step 410 corresponding to a second time interval. Second step410 is proximate first step 408 in a direction along the central axis ofthe staircase and offset from the first step in an angular direction 412around the central axis. The second time interval may be after the firsttime interval. An angular extent 414 of each of the plurality of stepsmay be the same. Staircase 400 may proceed similarly from the secondstep to a third step 416, and so on.

A magnitude 418 of each of the data elements (e.g., nodes) underlyingthe plurality of steps 404 is indicated by an axial extent of that stepalong central axis 406. In the example staircase topology shown in FIG.11, magnitude 418 of a fourth step 420 is less than the magnitude of asixth step 422, indicating that the value of the data element is largerduring the sixth time interval than during the fourth time interval.

Staircase topology 400 allows a user of the data visualization system tosee in one 3-D image how a single data element evolves over time. A datavisualization system may be configured to generate two or more staircasetopologies, each corresponding to a different data element, to comparethe evolution of the two or more underlying data elements.

For example, an underlying data set may correspond to election resultsfor a plurality of past elections. The staircase topology may be used toshow the total number of votes for the Democratic presidential nomineein a particular county over a number of previous elections. A second,similar staircase may show the corresponding data for the Republicanpresidential nominee in the same county, allowing for side-by-sidecomparison of the results over time.

Once staircase creature 400 has been created, a user may manipulate animage of the staircase, e.g., using a graphical user interface, byrotating the staircase or zooming in or out on a particular aspect ofthe staircase. Viewing the staircase from more than one vantage pointmay give a user a better appreciation for the time evolution of theunderlying data element.

Turning to FIG. 12, an annular or circular topology is generallyindicated at 450. Similar to the staircase topology, the annulartopology may be used to show how a single data element or node changesover time. Time progresses regularly along a vertical direction,indicated by arrow 452.

Alternately, as described above, the annular topology may be used toshow how an expression based on the underlying data set changes overtime. For example, an expression may be a mathematical result based onthe relationship between a first parent node and a second parent node,such as total revenue minus cost of goods sold. In this way, the changein the expression can be observed over time in a representation that isstatic with respect to time.

The annular topology 450 may include a plurality of annular rings 454.Each ring may correspond to a value of a particular data element orexpression during a time interval, with each ring sized to reflect thecorresponding value of the node or expression. Each subsequent ring maybe stacked on top of the previous ring such that the rings are coaxialalong a central axis 456.

A magnitude 458 of each of the plurality of annular rings 454 may beindicated by a radial extent of the annular ring away from the centralaxis 456. In the exemplary annular topology shown in FIG. 12, themagnitude 458 of a first annular ring 460 is less than the magnitude ofa subsequent nth annular ring 462, indicating that the value of theunderlying data element or expression has grown with time.

Each of the plurality of annular rings 454 may be an annulus with a hole464 centered on central axis 456. Alternately, each of the plurality ofrings 454 may be a solid disk without the central hole.

Similarly to the staircase topology described in reference to FIG. 11,the annular topology may allow the user of a data visualization systemto see in one image how a single data element or expression evolves overtime. Furthermore, viewing two or more annular topologies side-by-sidemay allow a user to compare the time evolution of the two or moreunderlying data elements or expressions.

Once an annular creature 450 has been created, a user may manipulate animage of the annular creature, perhaps by a graphical user interface, byrotating the creature or zooming in or out on a particular aspect of thecreature. Viewing the annular creature from more than one vantage pointmay give a user a better appreciation for the time evolution of theunderlying data element or expression.

FIGS. 13 and 14 depict various aspects of the fourth topology, alsoreferred to as the starburst or data flower topology, generallyindicated at 500. FIG. 13 depicts the layout of the topology and FIG. 14depicts an illustrative embodiment. Data flower topology 500 may be usedto show how related nodes or data elements change over time in a single,static representation. For example, a set of related nodes from ahierarchical data set at a first time may be mapped (e.g., in coplanarfashion, as shown in FIGS. 14-15) around the circumference of a cylinder502 having a long axis 504 at a first axial location 506. The same setof related nodes at a second time after the first time may be mappedaround the circumference of the cylinder at a second axial location 508offset from (e.g., above) the first location. That is, the data flowertopology may generally show time along an axial direction, indicated byarrow 510, substantially parallel to central long axis 504 of cylinder502. The second time may be followed along the long axis by a third timeat a third axial location 512, and so on.

A magnitude or value 514 of each data element at a given time may berepresented as the radial length or extent of a protruding element 516away from the long axis 504 of the cylinder 502. Positive values may berepresented as protruding elements extending away from the cylinder, andnegative values may be represented as protruding elements extendingtoward the central axis. Any appropriate number of data elements may berepresented around cylinder 502.

In the illustrative data flower shown in FIG. 14, a first parent node518 and an associated first set of child data nodes, generally indicatedat 520, are mapped onto cylinder 502 as protruding elements,specifically in this example as annular sectors extending radially fromthe cylinder. A second parent node 522 and an associated second set ofchild data nodes, generally indicated at 524, are also mapped onto thecylinder. Any appropriate number of parent nodes and their children maybe mapped onto the cylinder. First and second parent nodes 518 and 522may be siblings having a common parent node (not shown in FIG. 14), orthey may be unrelated. In some examples, a data flower creature mayinclude only data elements of a single generation of hierarchical data.

The data flower topology may allow a user of a hierarchical datavisualization system to see in one static image how a related set ofdata elements evolves over time. Once a data flower creature 500 hasbeen created, a user may manipulate an image of the data flower, perhapsby a graphical user interface, by rotating the data flower or zooming inor out on a particular aspect of the data flower. Viewing the dataflower creature from more than one vantage point may give a user abetter appreciation for the time evolution of the underlying dataelements.

FIG. 15 depicts various aspects of the topology referred to as a rose,generally indicated at 550. Rose topology 550 may be used to show howmore than one generation of hierarchical data evolves over time. In thistopology, time progresses axially, as indicated by arrow 552, generallyparallel to a central axis 554. Similar to the data flower creature, amagnitude 556 of a data element may be indicated in the rose topology bythe radial or annular dimension of a protruding element 558 (e.g.,annular sector) as measured from the central axis.

Rose topology 550 may include a plurality of levels 560. Each level 560may be generally perpendicular to central axis 554 and may correspond toa time interval. The plurality of levels may be spaced from one anotheralong the central axis, for example the levels may be stackedsequentially along the central axis. Each level 560 may optionallyinclude a central disk 562 having central axis 554 as a symmetry axis,which may represent a parent node, an expression comprising one or morenodes, or any other suitable information.

The rose topology may include a first reference cylinder 564 aligned tocentral axis 554. First reference cylinder 564 may be similar tocylinder 502 in the data flower topology described in reference to FIGS.13 and 14. A set of data nodes 566 may be mapped around thecircumference of the first reference cylinder. For example, if thecentral disk 562 represents a node, the other nodes mapped around thecircumference of the first reference cylinder may be the children ofthat central node. In another example, if a central disk is notincluded, the nodes mapped onto the first reference cylinder may be anunrelated set of parent nodes.

Each level 560 of the rose topology 550 may represent a set of datanodes at a different time. First reference cylinder 564 of the rosetopology, along with the values represented on the first cylinder, maybe similar to the data flower topology 500 described in reference toFIGS. 13 and 14.

The rose topology may include a second reference cylinder 568 aligned tocentral axis 554 (i.e., concentric with cylinder 562) and having alarger radius than the first cylinder. A second set of data elements 570may be mapped around the circumference of the second reference cylinder.The second data elements mapped to the second reference cylinder 568 maybe of a later generation than the data elements mapped to the firstreference cylinder 564. In other words, second data elements 570 may bethe children of data elements 566. Each data element 566 mapped onto thefirst reference cylinder may define an angular extent for the family ofdata associated with that data element. In the example rose topologyshown in FIG. 15, there are four data elements 566 mapped to firstreference cylinder 564, and each of these data elements spans ninetydegrees around central axis 554. The children of each parent dataelement may span the same angular extent as their parent. For example,child data elements 572, 574, and 576 are children to data element 578and are aligned angularly with data element 578. Similarly, child dataelements generally indicated at 580 are aligned with their parent dataelement 582.

As with the data flower topology described above, positive values ofdata elements in the rose topology 550 may be represented as protrudingelements extending away from the central axis and negative valuesrepresented as extending toward the central axis. In the example rosetopology shown in FIG. 15, child data element 574 has a positive valueand child data element 576 has a negative value. If a particular dataelement has a value of zero, a blank space may be left to indicate thezero value. For example, child data elements 572, 574, and 576 may havea sibling with a value of zero, indicated by empty space 584.

Rose topology 550 may accommodate any number of generations ofhierarchical data. For example, a third generation of data may berepresented on a third coaxial/concentric cylinder similar to the secondgeneration of data mapped to second reference cylinder 568. If dataelement 574 has children of its own, those child data elements may bemapped onto the third cylinder within the same angular span as dataelement 574. Any number of cylinders of increasing radii may be includedin the rose topology.

Rose topology 550 may allow a user of a hierarchical data visualizationsystem to see, in one 3-D image, how the members of a generation of dataelements relate to one another, how that generation relates tosubsequent or previous generations, and how those data elements changewith time. After rose creature 550 has been generated, a user maymanipulate an image of the rose, perhaps by a graphical user interface,by rotating the rose or zooming in or out on a particular aspect of therose. Viewing the rose from more than one vantage point may give a usera better appreciation for the time evolution of the underlying dataelements.

FIG. 16 depicts various aspects of a topology referred to as the reversehex index (RHI) topology, generally indicated at 600. The RHI topologymay be used to show how the values of related nodes or data elementschange over time in a single, static representation. For example, a setof related nodes from a hierarchical data set at a first time may bemapped along a first horizontal axis 602 of a rectangular grid pattern604. The same set of related nodes at a second time after the first timemay be mapped along the first horizontal axis 602 of grid 604 but spacedalong a second horizontal axis 606. That is, in the RHI topology, timemay progress generally along the second horizontal axis 606. The secondtime may be followed along the second horizontal axis 606 by a thirdtime, and so on.

A magnitude or value 608 of each data element may be represented as alinear height of a column or bar 610 above the grid pattern 604 along avertical axis 612. Any appropriate number of data elements may berepresented along the first horizontal axis 602. The represented dataelements may include related data elements of one or more generations ofhierarchical data or may include unrelated data elements.

Time may or may not proceed strictly linearly along the secondhorizontal axis 606. In one example, a data element 614 may indicate theamount of money a couple spends on food in a given week. Every twelveweeks along the second horizontal axis 606 may be an intermediate dataelement 616 indicating the sum total of food expenditures during thepreceding twelve weeks. After four intermediate data elements have beenshown a total year data element 618 may show the sum total of foodexpenditures 618 being the additive sum of the four intermediate dataelements 616. That is, time may proceed generally along the secondhorizontal axis 606 with interludes or interruptions for theaccumulating of data. An adjacent row 620 in the RHI topology mayrepresent the time evolution of a related data element. For example, row620 may represent the couple's weekly expenditures on fuel. In anotherexample, row 620 may represent the couple's weekly expenditures on foodfrom the previous year, thereby allowing for a side-by-side comparison.

The RHI topology may allow a user of a hierarchical data visualizationsystem to see in one image how a related set of data elements evolvesover time. Once an RHI creature 600 has been created, a user maymanipulate an image of the creature, perhaps by a graphical userinterface, by rotating the creature or zooming in or out on a particularaspect of the creature. Viewing the RHI creature from more than onevantage point may give a user a better appreciation for the timeevolution of the underlying data elements.

FIG. 17 depicts various aspects of a topology referred to as thebuilding topology, generally indicated at 650. The building topology maybe used to show the values of one or more parent data elements or nodesand up to one generation of child data for each parent node. Forexample, a rectangular grid pattern 652 may include a first row 654representing a first set of underlying data elements. The first row mayinclude a first building 656 representing a first parent node and aplurality of child buildings 658 representing the child nodes of theparent node. The grid pattern 652 may include a second row 660representing a second set of underlying data elements including a secondparent node 662 and the associated child nodes 664, etc.

Each building in the building topology may be divided into a regularpattern of three dimensional blocks 668, each of which may represent anappropriate value. A magnitude or value of each data element representedby a building may correspond to a number of consistently-sized blocks668 included in the building. Although this method may introducerounding errors, the block size and parameters may be selected based onpermissible rounding error or other factors.

Each of the buildings may have a common footprint of blocks. Forexample, in the exemplary building topology shown in FIG. 17, eachbuilding has a four-by-four footprint of blocks 668 on the rectangulargrid pattern 652. The blocks may represent value only, or may have aparticular meaning based on their disposition within the footprint. Forexample, a building may have a three-by-four footprint of twelve blocks,with each block representing a value associated with a month of theyear. The magnitude of each data element may be roughly estimated by avertical extent of each building along a vertical axis 670 disposedperpendicular to the grid pattern. Blocks 668 are shown as cubes in thisexample, but may have any suitable size or shape. For example, blocks668 may be rectangularly cuboidal.

Building topology 650 may be used to show cumulative value of dataelements. For example, child data elements 658, 664, etc. may beindependent data elements, and the associated parent data elements 658,662, etc., may be the sum of the associated children. The use of blocks668 to indicate value may make such a representation particularlyintuitive for a user of a hierarchical data visualization system.

Building topology 650 may represent a time slice of a hierarchal dataset. Similar building topologies may be created to represent the sameunderlying data elements at later or earlier times. Time evolution ofthe underlying data set may be displayed as an animation of thesebuilding topologies, with the height of each building and/or the numberof blocks 668 included in each building changing with time during theanimation. If one or more building topologies have been created, a usermay manipulate an image of the buildings, e.g., by a graphical userinterface, by rotating the pattern or zooming in or out on a particularaspect of the pattern. Viewing the building topology from more than onevantage point may give a user a better appreciation for the parent-childrelationships of the underlying data elements, potentially even the timedependence of those relationships.

Drill Up:

This section describes various aspects of a helix topology, describedbriefly above, which may allow a user to further manipulate, interactwith, and/or “drill up” with respect to a data set. The helix topologymay be used to appreciate how various data elements are related to oneanother on a larger scale, show a progression over time, performsequential processing of data, and/or any other appropriate analysis ofthe underlying data; see FIG. 18.

FIG. 18 depicts various aspects of the helix topology, generallyindicated at 700. The helix topology may show progression of a root nodeand the associated child data over time, may illustrate and/orfacilitate sequential processing of data, and/or may show multiplerelated hex visualizations, among others.

Helix topology 700 may show related sets of data elements as spacedalong a spiraling helix 702. Helix 702 spirals along the Z axis and haseither a constant or expanding radius in the X-Y dimension. Accordingly,helix 702 may have a constant radius as viewed along a vertical axis 704or may have an increasing or decreasing radius. That is, projectinghelix 702 into the X-Y (i.e., horizontal) plane may yield a circle or aspiral.

In some examples, helix topology 700 may be used to expand or spread outthe elements of a hex topology, such as visualization 200 (see FIG. 5).The spatial relationships (e.g., edge to edge) between a parent node andthe associated generations of children may be the same as in anon-expanded hex topology, but each spiral arm (also referred to as abranch or family) may be spaced from the other arms along the helix 702.The helix 702 may intersect each branch at a parent node. Separating therespective branches along the helix may allow each branch to includemore generations of data than in a standard hex visualization withoutadjacent branches colliding with one another.

In some examples, helix topology 700 may be used to show progression(e.g., over time) of a single spiral arm of a hex visualization. Forexample, the helix topology may be used to show how the values of afamily of nodes or data elements change over time in a single, staticrepresentation, as opposed to an animation or flipbook-styleinteraction.

In some examples, helix topology 700 may be used to show multiplerelated hex visualizations. Instead of having arms of a single hextopology spaced along helix 702, entire hex topologies may be spacedalong helix 702. These whole hex tolopogies may represent related setsof hierarchical data or may represent a time- or other variable-basedevolution of one set of hierarchal data. That is, the helix topology maybe used to show how the values of an entire hierarchal data set changesover time in a single, non-animated, interactive, 3-D representation.

In some examples, helix topology 700 may be used to illustrate offacilitate the sequential processing of data. In addition torepresenting and/or storing hierarchical data, tessellated datavisualization systems according to the present teachings may illustrateand/or be used as hierarchical decision or processing machines. Forexample, each node may include executable instruction(s) (e.g., adecision engine) configurable to produce a solution or output based oninputs from one or more other nodes.

When used in this manner, a tessellated system may be considered a dataprocessor and/or decision tree. A plurality of outer nodes in a hex datavisualization, for example, may coalesce or otherwise converge on acentral “answer” or set of results of the program at the root nodes.Multiple hex data visualizations (or portions thereof) may be stacked orotherwise connected to each other (e.g., in a helix), such that theoutput of one hex level is utilized as an input at the next hex level.

For example, an arm 710 of a helix visualization may include a parentnode 712 and associated generations of children 714. Parent node 712 maybe a calculated value and the associated generations of children 714 maycomprise data that was used to calculate the value 712. A subsequentparent node 716 may depend on its own child data 718 as well as thecalculated value 712. The dependency of parent node 716 on parent node712 may be established and/or represented by the intersection of helix702 with both parent nodes. Thus, a sequential processing of data, wherecalculations depend on the results of previously made calculations, maybe represented by the helix topology.

In some examples, a calculation that results in a value for a parentnode may be associated with a child node during a later calculation. Inthese cases, helix 702 may establish and/or illustrate the situation byintersecting a branch of the helix topology at the child node inquestion, rather than at the parent node.

In light of the above description, it should be seen that each node maycomprise an array of properties and functions, and that subsets of theseproperties and functions may be called upon, depending on the selectedmodality or functionality desired. In other words, each node or elementof the present disclosure may be versatile in an object-oriented sense,in that it can morph between visual, computational, logical, structural,and/or modular functionality.

Once a helix visualization 700 has been created, a user may manipulatean image of the helix, e.g., using a graphical user interface, byrotating the helix or zooming in or out on a particular aspect of thehelix. Viewing the helix from more than one vantage point may give auser a better appreciation for the relationships of the underlying dataelements. As with other topologies described herein, multiple helixvisualizations may be created and presented as an animation, e.g., toindicate the passage of time.

Illustrative Algorithm to Process and Visualize Hierarchical Data

This section describes a method for processing and visualizinghierarchical data; see FIG. 19. Aspects of tessellated datavisualization systems (see above descriptions), data processing systems,and/or computer network systems may be utilized in the method stepsdescribed below. Where appropriate, reference may be made to componentsand systems (described herein) that may be used in carrying out eachstep. These references are for illustration, and are not intended tolimit the possible ways of carrying out any particular step of themethod.

FIG. 19 is a flowchart illustrating operations performed by oneembodiment, and may not recite the complete process or all steps of theprogram. FIG. 19 depicts multiple steps of a method, generally indicatedat 800, which may be performed in conjunction with data visualizationsystems according to aspects of the present disclosure. Although varioussteps of method 800 are described below and depicted in FIG. 19, thesteps need not necessarily all be performed, and in some cases may beperformed in a different order than the order shown. In some examples,one or more steps from method 800 may be performed in conjunction withone or more steps from methods 900 and/or 1000, described below.

The following steps are configured to be performed at least in part by adata processing system and/or at least in part by a computer network(see FIGS. 21 and 22, and detailed descriptions below). Accordingly,they may be interpreted as programmed instructions to be executed by oneor more processors. Data being operated on may be disposed at a local orremote data store.

At step 802, an existing data cube or multidimensional dataset isqueried and data is received. For example a visualization systemprocessor may query a data store containing a dataset. The dataset maycontain hierarchical data, and/or data otherwise capable of beingaggregated into a hierarchical structure, such as one or more datatrees. This step may include selecting from a plurality of possible datastores and/or cubes.

Step 802 may include selecting a desired topology (e.g., basictessellated hex with 30-degree Z-offset, etc.). In some examples,topology selection may be performed as a separate step, a later step, oras a pre-selected option, default setting, or the like, performedoutside of method 800.

Step 802 may include selecting an aggregation method. For example, datafrom the dataset may be aggregated as one or more summations, averagevalues, cumulative values, etc. Note that aggregation, as used herein,may include combinations of and/or calculations based on the data, andmay include relative value, delta (e.g., change in value), percent,cumulative, and the like, or any combination of these.

At step 804, the queried data from step 802 is processed according tothe selections of step 802, thereby aggregating and/or consolidatingand/or allocating the data to form a second data cube. Step 804 mayinclude generating a temporary data store for storing the second datacube.

Step 804 may include attaching a respective index and/or positioninginformation to each node or data element. In other words, the selectedtopology may define a set of possible positions (e.g., node locations ina tessellated hex grid/map or on an imaginary rose cylinder). Each datanode may be assigned a position on the grid, e.g., based on itsrelationship to other points. For example, in a tessellated columnvisualization, root nodes will be assigned the central positions, firstlevel children will be assigned adjacent to the root nodes, etc.

Step 804 may include generation of height information for each node,e.g., corresponding to the magnitude or other aspect of the dataunderlying the node. As described above, height information maycorrespond to the Z-axis for a tessellated column creature, the radialdimension for a rose creature, etc., and may be positive or negativedepending on the underlying value being represented.

Step 804 may include, e.g., if an animation is desired, generation ofmultiple “frames” of the height information, such that sequentialdisplay of the heights will result in an animation of the informationover time (or over whatever index corresponds to the differentmagnitudes for the same node, typically shown in a table as columnheadings).

At step 806, one or more aspects of the data visualization may bedisplayed in two, three, and/or four dimensions, on a graphical userinterface (GUI) or other (e.g., holographic) display, based on theselected topology and the aggregated data.

At step 808, a user may optionally modify and/or otherwise interact withthe visualization to enhance analysis and understanding. For example,additional topologies may be selected and activated to drill down orotherwise display secondary information. Data may be visualized as aseries of frames that are playable as an animation. The animation mayplay as a video and/or in stepwise fashion under the user's control.Additional visual controls may be available, such as magnification/zoom,rotation, panning, revolution, inversion, and the like, or anycombination of these.

Illustrative Algorithm to Generate Tessellated Column Topology

This section describes a method for visualizing hierarchical dataaccording to a tessellated column topology; see FIG. 20. Aspects oftessellated data visualization systems (see above descriptions), dataprocessing systems, and/or computer network systems may be utilized inthe method steps described below. Where appropriate, reference may bemade to components and systems (described herein) that may be used incarrying out each step. These references are for illustration, and arenot intended to limit the possible ways of carrying out any particularstep of the method.

FIG. 20 is a flowchart illustrating operations performed by oneembodiment, and may not recite the complete process or all steps of theprogram. FIG. 20 depicts multiple steps of a method, generally indicatedat 900, which may be performed in conjunction with data visualizationsystems according to aspects of the present disclosure. Although varioussteps of method 900 are described below and depicted in FIG. 20, thesteps need not necessarily all be performed, and in some cases may beperformed in a different order than the order shown.

The following steps are configured to be performed at least in part by adata processing system and/or at least in part by a computer network(see FIGS. 22 and 23, and detailed descriptions below). Accordingly,they may be interpreted as programmed instructions to be executed by oneor more processors. Data being operated on may be disposed at a local orremote data store.

At step 902, one or more data elements of a data set (e.g., ahierarchical data set) are received by the system. Each of these dataelements may include an associated value, e.g., a numerical value.Receiving the one or more data elements may include receiving data noderelationship information. For example, parent-child and/or siblingrelationship information may be provided with or as part of the dataset. For example, hierarchy indices, time stamps, categorizations, andthe like may be received in step 902.

At step 904, hierarchical data nodes are identified and/or recognized bythe system. Specifically, data nodes may each include one or more dataelements combined according to selected rules to produce a quantitativevalue. For example, a data node may be the sum of all transactionsoccurring within a specific business department. Quantitative values mayinclude percentages, dollar amounts, population counts, delta values,results of formulaic expressions, and/or the like. In some examples, thequantitative value associated with a data node may be non-numerical. Forexample, a quantitative value may be selected from a set of definedranges, such as low/medium/high or cold/warm/hot, or letter grades, suchas A/B/C/D/F, in which each designation equates to a defined quantity orrange of numerical values.

In addition to a value, each data node may also have a relationship toone or more other data nodes. These relationships include parent-childrelationships indicating which child nodes may be combined to producewhich parent nodes. Child nodes having the same parent may be referredto as sibling nodes. A node that has no parents may be referred to as aroot node. A node that has no children may be referred to as a leafnode. Step 904 includes identifying root nodes and one or moregenerations of child nodes depending from those root nodes.

Data nodes and/or their associated relationships may be identified byany suitable method. In some examples, data nodes and/or relationshipsmay be predefined and/or inherent in the data set, in which caseinformation identifying the nodes and relationships may be received withthe data in step 902 (or separately). In some examples, data nodesand/or relationships may be identified dynamically by the system, and/orby a user. Identifying information may include the use of one or moreindices, such as the commonly used decimal-point hierarchical indexingsystem, also referred to as dot notation (e.g., 1.1, 2.4.1, etc.).

At step 906, a multi-dimensional graphical object (i.e., avisualization) is generated by the system to illustrate the one or morerelationships and to illustrate a respective quantitative valueassociated with each of the data nodes. Some or all of the data nodesmay be represented. For example, a subset of the data nodes may beillustrated. In some examples, the selected data nodes may be modified(e.g., aggregated, or combined according to selected rules oroperations), and the resulting modified data nodes may be illustrated.

Generating the graphical object includes the following steps:

At step 908, a tessellatable shape is selected by the system. Forexample, a tessellatable shape may be selected based on userpreferences. For example, a hexagonal shape may be selected. In someexamples, the system may have a defined, preselected, and/or defaulttessellatable shape, in which case step 908 may be bypassed or optional.

At step 910, one or more of the root nodes identified in step 904 arerepresented as columns arranged in a circular, edge-to-edge cluster,each of the columns having the tessellatable cross-sectional shapeselected in step 908 (or predefined or preselected, e.g., as in adefault tessellatable shape). The columns are arranged such that thecross-sectional shape lies in an X-Y plane. The height of each column isdefined as its height relative to the X-Y plane along a Z-axisorthogonal to the X-Y plane. In some examples, a gap may be presentbetween the proximal edges of any two adjacent columns. The size of thisgap may be selectable and/or variable. If a hexagonal shape is selectedin step 908, then hexagonal columns may be arranged in six hexagonalnode locations to form a substantially circular formation or cluster.Fewer than six such columns may be represented in these six nodelocations.

At step 912, one or more second generation child nodes may berepresented (e.g., mapped) in relation to the associated parent rootnode. The second generation child nodes are represented as columns, andmay have the same cross sectional shape as the parent root nodes. If thesecond generation child nodes have the same cross sectional shape as theroot nodes, the nodes may all be mapped onto the same planar,tessellated grid. The second generation child nodes are mapped onto thegraphical display such that the child nodes extend single file from oneunoccupied edge of the parent root node. In some examples, the childnodes have edge-to-edge adjacency. In some examples, the child nodesextend radially from the parent root node. If the parent root node has ahexagonal shape (i.e., six edges), the second generation child nodes mayextend from any one of the three outer edges (two other edges beingoccupied by adjacent root nodes and the remaining inner edge facingtoward the middle of the cluster). Choosing the middle of the threeouter edges will cause the child nodes to extend radially outward.Choosing one of the other outer edges will cause the child nodes toextend in a clockwise or counterclockwise direction, when viewed normalto the X-Y plane.

Optional step 914 includes mapping one or more third generation childnodes in relation to their parent, which is one of the second generationchild nodes. The third generation child nodes are represented ascolumns, and may have the same cross sectional shape as the root nodes.For the purposes of this mapping, the second generation child nodes areconsidered to have two opposing edges occupied, whether or not parent orsibling nodes are present at those edges. Accordingly, the thirdgeneration child nodes are mapped onto the graphical display such thatthese child nodes extend single file from one unoccupied edge of theirrespective parent node. In some examples, the child nodes haveedge-to-edge adjacency. In some examples, all third generation childnodes for any given parent node are mapped from the same relative edgeon each respective parent node.

At step 916, the height of each column is set to correspond to itsrespective associated data node value. Positive values may result incolumns having a height that extends in a positive Z direction withrespect to the X-Y plane. Negative values may result in columns having aheight that extends in a negative Z direction with respect to the X-Yplane. In some examples, column heights may extend along a same Zdirection corresponding to an absolute value of the underlying data, andpositive or negative values may be distinguished in some other fashion,e.g., by color coding. Step 916 may be performed simultaneously withmapping of each column.

At step 918, the resulting multi-dimensional graphical object istransmitted for display. For example, the graphical object may betransmitted to a GUI. For example, the graphical object may be displayedon a screen. In some examples, the graphical object may beholographically projected into real space.

At optional step 920, the resulting multi-dimensional graphical objectmay be manipulated. For example, the system may receive commands from auser (e.g., via a GUI) to rotate, zoom, pan, etc., and the system mayrespond accordingly.

Illustrative Algorithm to Generate Rose Topology

This section describes a method for visualizing hierarchical dataaccording to a rose topology; see FIG. 21. Aspects of tessellated datavisualization systems (see above descriptions), data processing systems,and/or computer network systems may be utilized in the method stepsdescribed below. Where appropriate, reference may be made to componentsand systems (described herein) that may be used in carrying out eachstep. These references are for illustration, and are not intended tolimit the possible ways of carrying out any particular step of themethod.

FIG. 21 is a flowchart illustrating operations performed by oneembodiment, and may not recite the complete process or all steps of theprogram. FIG. 21 depicts multiple steps of a method, generally indicatedat 1000, which may be performed in conjunction with data visualizationsystems according to aspects of the present disclosure. Although varioussteps of method 1000 are described below and depicted in FIG. 21, thesteps need not necessarily all be performed, and in some cases may beperformed in a different order than the order shown.

The following steps are configured to be performed at least in part by adata processing system and/or at least in part by a computer network(see FIGS. 22 and 23, and detailed descriptions below). Accordingly,they may be interpreted as programmed instructions to be executed by oneor more processors. Data being operated on may be disposed at a local orremote data store.

At step 1002, one or more data elements of a hierarchical data structureare received, wherein the hierarchical data structure includes root nodedata, at least one level of child node data, and relationships betweenthe root node data and the at least one level of child node data. Eachof the one or more data elements includes a plurality of valuescorresponding to a plurality of time intervals.

At step 1004, hierarchical data nodes are identified and/or recognizedby the system. This step may be substantially identical to step 904above.

Step 1006 includes generating, via the processing device, athree-dimensional virtual object to illustrate the plurality of valuesof the one or more data elements corresponding to the plurality of timeintervals.

Generating the three-dimensional virtual object includes:

At step 1008, defining a first reference cylinder having a first radius,a central axis, and a plurality of axial locations along the centralaxis;

At step 1010, representing a first value of a first data element duringa first time interval as a first protruding member extending from thefirst radius of the first reference cylinder at a first axial andangular location, the first protruding member having a radial extentfrom the first radius corresponding to the value of the first dataelement during the first time interval;

At step 1012, representing a second value of the first data elementduring a second time interval as a second protruding member extendingfrom the first radius of the first reference cylinder at a second axialand angular location, the second time later than the first time, thesecond axial and angular location spaced from the first axial andangular location along the central axis, the second protruding memberhaving a radial extent from the first radius corresponding to the valueof the first data element during the second time interval; and

At step 1014, representing a third value of a second data element duringthe first time interval as a third protruding member extending from thefirst radius of the first reference cylinder at a third axial andangular location, the third axial and angular location spaced from thefirst axial and angular location around the central axis, the thirdprotruding member having a radial extent from the first radiuscorresponding to the value of the second data element during the firsttime interval.

Step 1016 includes transmitting, via the processing device, thethree-dimensional virtual object for presentation on a display.

Step 1018 includes manipulating the graphical object, e.g., using agraphical user interface. See description of step 920 above.

Method 1000 may be continued by representing additional data elementsaround a circumference of the first reference cylinder at additionaltimes along a height of the cylinder. The data elements representedaround the first reference cylinder's circumference may include anycombination of root nodes, parent nodes, and child nodes of thehierarchical data set. In some examples, the represented data may besiblings of a common parent node. In some example, more than onegeneration of hierarchical data may be represented on the firstreference cylinder. Nodes represented around the cylinder circumferencemay also be represented along the cylinder height, thereby showing theprogress of the nodes over any appropriate number of time intervals.

Method 1000 may be continued by defining a second reference cylinderhaving a second radius greater than the first radius, the same centralaxis as the first reference cylinder, and a plurality of axial locationsalong the central axis. Additional data elements may be representedaround and along the second reference cylinder in a similar manner aswith respect to the first reference cylinder.

The second reference cylinder may include representations of additionaldata elements or additional generations of data elements from thehierarchical data set. In some examples, child nodes of a parent nodemay be disposed on the second reference cylinder within the same angularspan around the central axis as their parent node on the first referencecylinder. In some examples the data represented on the second referencecylinder may not have familial relationships with the data representedon the first reference cylinder. Any appropriate number of additionalcoaxial reference cylinders may be added to the virtual object in asimilar manner.

Method 1000 may be continued by representing the value of an additionaldata element or of an expression, at each of the time intervals, as aplurality of central disks disposed within the first reference cylinderand having the central axis as a symmetry axis. Each central disk mayrepresent a data element, such as a parent node or a root node, or mayrepresent an expression based on the data represented on the one or morereference cylinders (or elsewhere). Each central disk may be sized tohave a radial extent from the central axis corresponding to the value ofthe data element or expression during the corresponding time interval.In some examples, the reference cylinders may be resized as needed toaccommodate the central disks therein.

Image-based Data Derivation

In some examples, one or more of the visual topologies described hereinmay exist (or be caused to exist) only as a graphical object (e.g., a3-D image) isolated from the underlying data. It may be useful, in theseand other situations, to be able to reverse engineer the data based onthe graphical object (e.g., image) alone. In some examples, as may bethe case with cutting edge memory storage techniques, it may be moreefficient or otherwise advantageous to store the information as animage, series of images, holographic image, or multi-dimensional image,as opposed to storing the underlying data and dynamically generating thegraphical object.

Accordingly, dynamic generation of data from the graphical object may befacilitated by providing a way to translate or interpret the visualimage into numerical information. For example, a scale or othermeasuring information may be displayed with the visual image, orembedded in it. For example, a scale may indicate that a certain amountof visual “volume” in a column corresponds to a certain numericalquantity. Such a scale may be used to visually assess the displayedcolumns and ascertain a (possibly estimated) underlying value. Applyingthe scale to each column in the displayed graphical object, and possiblycross-referencing known relationships (e.g., children whose values areknown to add up to a parent's value), may facilitate a translation ofthe image into the underlying data.

In a similar method, the items displayed in a graphical object may beshown as a collection of defined building blocks (see, e.g., FIG. 17).In examples having this feature, derivation of underlying values may beperformed in a straightforward manner, by counting or extrapolating thenumber of such blocks and translating the block count into a numericalvalue. Such methods may introduce rounding errors, depending on thegranularity of the building blocks with respect to the data.

In some examples, scaling information, or even the underlying dataitself, may be incorporated into the image using machine-readableencoded imagery. For example, one or more 2D barcodes (e.g., QR Codes)may be included in the generated image. Scaling information and/or someor all of the underlying data may be encoded in these barcodes.

Illustrative Data Processing System

As shown in FIG. 21, this example describes a data processing system1200 (also referred to as a computer) in accordance with aspects of thepresent disclosure. In this example, data processing system 1200 is anillustrative data processing system suitable for implementing aspects ofdata visualization systems according to the present teachings. Morespecifically, in some examples, devices that are embodiments of dataprocessing systems (e.g., smart phones, tablets, personal computers) maybe used to perform methods and/or display and interact with graphicalobjects, such as those in the systems and methods described above.

In this illustrative example, data processing system 1200 includescommunications framework 1202. Communications framework 1202 providescommunications between processor unit 1204, memory 1206, persistentstorage 1208, communications unit 1210, input/output (I/O) unit 1212,and display 1214. Memory 1206, persistent storage 1208, communicationsunit 1210, input/output (I/O) unit 1212, and display 1214 are examplesof resources accessible by processor unit 1204 via communicationsframework 1202.

Processor unit 1204 serves to run instructions that may be loaded intomemory 1206. Processor unit 1204 may be a number of processors, amulti-processor core, or some other type of processor, depending on theparticular implementation. Further, processor unit 1204 may beimplemented using a number of heterogeneous processor systems in which amain processor is present with secondary processors on a single chip. Asanother illustrative example, processor unit 1204 may be a symmetricmulti-processor system containing multiple processors of the same type.

Memory 1206 and persistent storage 1208 are examples of storage devices1216. A storage device is any piece of hardware that is capable ofstoring information, such as, for example, without limitation, data,program code in functional form, and other suitable information eitheron a temporary basis or a permanent basis.

Storage devices 1216 also may be referred to as computer-readablestorage devices in these examples. Memory 1206, in these examples, maybe, for example, a random access memory or any other suitable volatileor non-volatile storage device. Persistent storage 1208 may take variousforms, depending on the particular implementation.

For example, persistent storage 1208 may contain one or more componentsor devices. For example, persistent storage 1208 may be a hard drive, aflash memory, a rewritable optical disk, a rewritable magnetic tape, orsome combination of the above. The media used by persistent storage 1208also may be removable. For example, a removable hard drive may be usedfor persistent storage 1208.

Communications unit 1210, in these examples, provides for communicationswith other data processing systems or devices. In these examples,communications unit 1210 is a network interface card. Communicationsunit 1210 may provide communications through the use of either or bothphysical and wireless communications links.

Input/output (I/O) unit 1212 allows for input and output of data withother devices that may be connected to data processing system 1200. Forexample, input/output (I/O) unit 1212 may provide a connection for userinput through a keyboard, a mouse, and/or some other suitable inputdevice. Further, input/output (I/O) unit 1212 may send output to aprinter. Display 1214 provides a mechanism to display information to auser.

Instructions for the operating system, applications, and/or programs maybe located in storage devices 1216, which are in communication withprocessor unit 1204 through communications framework 1202. In theseillustrative examples, the instructions are in a functional form onpersistent storage 1208. These instructions may be loaded into memory1206 for execution by processor unit 1204. The processes of thedifferent embodiments may be performed by processor unit 1204 usingcomputer-implemented instructions, which may be located in a memory,such as memory 1206.

These instructions are referred to as program instructions, programcode, computer usable program code, or computer-readable program codethat may be read and executed by a processor in processor unit 1204. Theprogram code in the different embodiments may be embodied on differentphysical or computer-readable storage media, such as memory 1206 orpersistent storage 1208.

Program code 1218 is located in a functional form on computer-readablemedia 1220 that is selectively removable and may be loaded onto ortransferred to data processing system 1200 for execution by processorunit 1204. Program code 1218 and computer-readable media 1220 formcomputer program product 1222 in these examples. In one example,computer-readable media 1220 may be computer-readable storage media 1224or computer-readable signal media 1226.

Computer-readable storage media 1224 may include, for example, anoptical or magnetic disk that is inserted or placed into a drive orother device that is part of persistent storage 1208 for transfer onto astorage device, such as a hard drive, that is part of persistent storage1208. Computer-readable storage media 1224 also may take the form of apersistent storage, such as a hard drive, a thumb drive, or a flashmemory, that is connected to data processing system 1200. In someinstances, computer-readable storage media 1224 may not be removablefrom data processing system 1200.

In these examples, computer-readable storage media 1224 is a physical ortangible storage device used to store program code 1218 rather than amedium that propagates or transmits program code 1218. Computer-readablestorage media 1224 is also referred to as a computer-readable tangiblestorage device or a computer-readable physical storage device. In otherwords, computer-readable storage media 1224 is a media that can betouched by a person.

Alternatively, program code 1218 may be transferred to data processingsystem 1200 using computer-readable signal media 1226. Computer-readablesignal media 1226 may be, for example, a propagated data signalcontaining program code 1218. For example, computer-readable signalmedia 1226 may be an electromagnetic signal, an optical signal, and/orany other suitable type of signal. These signals may be transmitted overcommunications links, such as wireless communications links, opticalfiber cable, coaxial cable, a wire, and/or any other suitable type ofcommunications link. In other words, the communications link and/or theconnection may be physical or wireless in the illustrative examples.

In some illustrative embodiments, program code 1218 may be downloadedover a network to persistent storage 1208 from another device or dataprocessing system through computer-readable signal media 1226 for usewithin data processing system 1200. For instance, program code stored ina computer-readable storage medium in a server data processing systemmay be downloaded over a network from the server to data processingsystem 1200. The data processing system providing program code 1218 maybe a server computer, a client computer, or some other device capable ofstoring and transmitting program code 1218.

The different components illustrated for data processing system 1200 arenot meant to provide architectural limitations to the manner in whichdifferent embodiments may be implemented. The different illustrativeembodiments may be implemented in a data processing system includingcomponents in addition to and/or in place of those illustrated for dataprocessing system 1200. Other components shown in FIG. 21 can be variedfrom the illustrative examples shown. The different embodiments may beimplemented using any hardware device or system capable of runningprogram code. As one example, data processing system 1200 may includeorganic components integrated with inorganic components and/or may becomprised entirely of organic components excluding a human being. Forexample, a storage device may be comprised of an organic semiconductor.

In another illustrative example, processor unit 1204 may take the formof a hardware unit that has circuits that are manufactured or configuredfor a particular use. This type of hardware may perform operationswithout needing program code to be loaded into a memory from a storagedevice to be configured to perform the operations.

For example, when processor unit 1204 takes the form of a hardware unit,processor unit 1204 may be a circuit system, an application specificintegrated circuit (ASIC), a programmable logic device, or some othersuitable type of hardware configured to perform a number of operations.With a programmable logic device, the device is configured to performthe number of operations. The device may be reconfigured at a later timeor may be permanently configured to perform the number of operations.Examples of programmable logic devices include, for example, aprogrammable logic array, a field programmable logic array, a fieldprogrammable gate array, and other suitable hardware devices. With thistype of implementation, program code 1218 may be omitted, because theprocesses for the different embodiments are implemented in a hardwareunit.

In still another illustrative example, processor unit 1204 may beimplemented using a combination of processors found in computers andhardware units. Processor unit 1204 may have a number of hardware unitsand a number of processors that are configured to run program code 1218.With this depicted example, some of the processes may be implemented inthe number of hardware units, while other processes may be implementedin the number of processors.

In another example, a bus system may be used to implement communicationsframework 1202 and may be comprised of one or more buses, such as asystem bus or an input/output bus. Of course, the bus system may beimplemented using any suitable type of architecture that provides for atransfer of data between different components or devices attached to thebus system.

Additionally, communications unit 1210 may include a number of devicesthat transmit data, receive data, or both transmit and receive data.Communications unit 1210 may be, for example, a modem or a networkadapter, two network adapters, or some combination thereof. Further, amemory may be, for example, memory 1206, or a cache, such as that foundin an interface and memory controller hub that may be present incommunications framework 1202.

The flowcharts and block diagrams described herein illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods, and computer program products according to variousillustrative embodiments. In this regard, each block in the flowchartsor block diagrams may represent a module, segment, or portion of code,which comprises one or more executable instructions for implementing thespecified logical function or functions. It should also be noted that,in some alternative implementations, the functions noted in a block mayoccur out of the order noted in the drawings. For example, the functionsof two blocks shown in succession may be executed substantiallyconcurrently, or the functions of the blocks may sometimes be executedin the reverse order, depending upon the functionality involved.

Illustrative Computer Network

As shown in FIG. 22, this example describes a general network dataprocessing system 1300, interchangeably termed a network, a computernetwork, a network system, a distributed network, a distributed dataprocessing system, or the like, in which illustrative embodiments ofdata visualization systems may be included. For example, various aspectsof the data visualization systems (and related methods) may beimplemented in or communicated using a computer network. It should beappreciated that FIG. 22 is provided as an illustration of oneimplementation and is not intended to imply any limitation with regardto environments in which different embodiments may be implemented. Manymodifications to the depicted environment may be made.

Network data processing system 1300 is a network of computers, each ofwhich is an example of data processing system 1200, and othercomponents. Network data processing system 1300 may include network1302, which is a medium configured to provide communications linksbetween various devices and computers connected together within networkdata processing system 1300. Network 1302 may include connections suchas wired or wireless communication links, fiber optic cables, and/or anyother suitable medium for transmitting and/or communicating data betweennetwork devices, or any combination thereof.

In the depicted example, a first network device 1304 and a secondnetwork device 1306 connect to network 1302, as does an electronicstorage device 1308. Network devices 1304 and 1306 are each examples ofdata processing system 1200, described above. In the depicted example,devices 1304 and 1306 are shown as server computers. However, networkdevices may include, without limitation, one or more personal computers,mobile computing devices such as personal digital assistants (PDAs),tablets, and smart phones, handheld gaming devices, wearable devices,tablet computers, routers, switches, voice gates, servers, electronicstorage devices, imaging devices, and/or other networked-enabled toolsthat may perform a mechanical or other function. These network devicesmay be interconnected through wired, wireless, optical, and otherappropriate communication links.

In addition, client electronic devices, such as a client computer 1310,a client laptop or tablet 1312, and/or a client smartdevice 1314, mayconnect to network 1302. Each of these devices is an example of dataprocessing system 1200, described above regarding FIG. 21. Clientelectronic devices 1310, 1312, and 1314 may include, for example, one ormore personal computers, network computers, and/or mobile computingdevices such as personal digital assistants (PDAs), smart phones,handheld gaming devices, wearable devices, and/or tablet computers, andthe like. In the depicted example, server 1304 provides information,such as boot files, operating system images, and applications to one ormore of client electronic devices 1310, 1312, and 1314. Clientelectronic devices 1310, 1312, and 1314 may be referred to as “clients”with respect to a server such as server computer 1304. Network dataprocessing system 1300 may include more or fewer servers and clients orno servers or clients, as well as other devices not shown.

Client smartdevice 1314 may include any suitable portable electronicdevice capable of wireless communications and execution of software,such as a smartphone or a tablet. Generally speaking, the term“smartphone” may describe any suitable portable electronic device havingmore advanced computing ability and network connectivity than a typicalmobile phone. In addition to making phone calls (e.g., over a cellularnetwork), smartphones may be capable of sending and receiving emails,texts, and multimedia messages, accessing the Internet, and/orfunctioning as a web browser. Smartdevices (e.g., smartphones) may alsoinclude features of other known electronic devices, such as a mediaplayer, personal digital assistant, digital camera, video camera, and/orglobal positioning system. Smartdevices (e.g., smartphones) may becapable of connecting with other smartdevices, computers, or electronicdevices wirelessly, such as through near field communications (NFC),BLUETOOTH®, WiFi, or mobile broadband networks. Wireless connectivelymay be established among smartdevices, smartphones, computers, and otherdevices to form a mobile network where information can be exchanged.

Program code located in system 1300 may be stored in or on a computerrecordable storage medium, such as persistent storage 108 in Example 1,and may be downloaded to a data processing system or other device foruse. For example, program code may be stored on a computer recordablestorage medium on server computer 1304 and downloaded for use to client1310 over network 1302 for use on client 1310.

Network data processing system 1300 may be implemented as one or more ofa number of different types of networks. For example, system 1300 mayinclude an intranet, a local area network (LAN), a wide area network(WAN), or a personal area network (PAN). In some examples, network dataprocessing system 1300 includes the Internet, with network 1302representing a worldwide collection of networks and gateways that usethe transmission control protocol/Internet protocol (TCP/IP) suite ofprotocols to communicate with one another. At the heart of the Internetis a backbone of high-speed data communication lines between major nodesor host computers. Thousands of commercial, governmental, educationaland other computer systems may be utilized to route data and messages.In some examples, network 1300 may be referred to as a “cloud.” In thoseexamples, each server 1304 may be referred to as a cloud computing node,and client electronic devices may be referred to as cloud consumers, orthe like. FIG. 22 is intended as an example, and not as an architecturallimitation for any illustrative embodiments.

Selected Examples

This section describes additional aspects and features of datavisualization systems and related methods, presented without limitationas a series of paragraphs, some or all of which may be alphanumericallydesignated for clarity and efficiency. Each of these paragraphs can becombined with one or more other paragraphs, and/or with disclosure fromelsewhere in this application, including the materials incorporated byreference in the Cross-References, in any suitable manner. Some of theparagraphs below expressly refer to and further limit other paragraphs,providing without limitation examples of some of the suitablecombinations.

A0. A method, implemented in a data processing system, the methodcomprising:

receiving, using a data processing system, one or more elements of adata set;

identifying, using a processor of the data processing system, aplurality of hierarchical data nodes of the data set, each of the datanodes having an associated quantitative value, and one or morerelationships between the data nodes, such that identifying the datanodes includes identifying a plurality of root nodes and one or moregenerations of child nodes;

generating, using the data processing system, a multi-dimensionalgraphical object illustrating the quantitative values of the data nodesand the one or more relationships between the data nodes;

wherein generating the graphical object includes:

-   -   representing the plurality of root nodes as a circular,        edge-to-edge cluster of columns, each such root node column        having a tessellatable cross-sectional shape;    -   representing, adjacent to a first root node of the plurality of        root nodes, one or more first child nodes having the first root        node as a parent, the one or more first child nodes represented        as respective child node columns extending single file from one        unoccupied edge of the first root node; and    -   setting a respective height of each root node column and of each        child node column, such that the respective height corresponds        to the quantitative value of the data node represented by the        respective column; and

transmitting the graphical object for display.

A1. The method of A0, wherein the circular, edge-to-edge cluster of rootnode columns defines an X-Y plane, the respective heights of each rootnode column being defined along a Z axis running orthogonal to the X-Yplane.

A2. The method of A1, wherein the tessellatable cross-sectional shape isdefined in the X-Y plane.

A3. The method of A0, wherein the root node columns and the child nodecolumns are represented isometrically.

A4. The method of A0, wherein generating the graphical object furtherincludes representing, adjacent to a first node of the first childnodes, one or more second child nodes having the first node as a parent,the one or more second child nodes represented as respective columnsextending single file from one unoccupied edge of the first node.

A5. The method of A4, wherein generating the graphical object furtherincludes representing, adjacent to a second node of the first childnodes, one or more third child nodes having the second node as a parent,the one or more third child nodes represented as respective columnsextending single file from one unoccupied edge of the second node, suchthat the third child nodes extend from the same relative edge of thesecond node as the second child nodes extend from the first node.

A6. The method of A5, wherein the circular, edge-to-edge cluster of rootnode columns defines an X-Y plane, and the second child nodes extendclockwise from the first node and the third child nodes extend clockwisefrom the second node, as viewed from a vantage point normal to the X-Yplane.

A7. The method of A0, wherein the first child nodes each have the samecross-sectional shape as the root node columns.

A8. The method of A0, wherein each of the root node columns is separatedfrom adjacent root node columns by a gap.

A9. The method of A0, wherein the tessellatable cross-sectional shape isa hexagon.

A10. The method of A0, wherein receiving the one or more elements of thedata set includes receiving data node relationship information.

A11. The method of A0, further including displaying the graphical objectthree-dimensionally in a graphical user interface.

B0. A data processing system for visualizing hierarchical data, thesystem comprising:

a processor;

a memory; and

a visualization program including a plurality of instructions stored inthe memory and executable by the processor to:

receive one or more elements of a data set;

identify a plurality of hierarchical data nodes of the data set, each ofthe data nodes having an associated quantitative value, and one or morerelationships between the data nodes, such that identifying the datanodes includes identifying a plurality of root nodes and one or moregenerations of child nodes;

generate a multi-dimensional graphical object illustrating thequantitative values of the data nodes and the one or more relationshipsbetween the data nodes, wherein generating the graphical object includesinstructions to:

-   -   represent the plurality of root nodes as a circular,        edge-to-edge cluster of columns, each such root node column        having a tessellatable cross-sectional shape;    -   represent, adjacent to a first root node of the plurality of        root nodes, one or more first child nodes having the first root        node as a parent, the one or more first child nodes represented        as respective child node columns extending single file from one        unoccupied edge of the first root node; and    -   set a respective height of each root node column and of each        child node column, such that the respective height corresponds        to the quantitative value of the data node represented by the        respective column; and

transmit the graphical object for presentation on a display.

B1. The system of B0, further including a display having a graphicaluser interface (GUI), the display being in communication with theprocessor such that the display is configured to receive the graphicalobject and present the graphical object in the GUI.

B2. The system of B1, wherein the display is remote from the processor.

B3. The system of B0, wherein the graphical object is transmitted forpresentation over a data processing network.

B4. The system of B0, wherein the circular, edge-to-edge cluster of rootnode columns defines an X-Y plane, the respective heights of each rootnode column being defined along a Z axis running orthogonal to the X-Yplane.

B5. The system of B4, wherein the tessellatable cross-sectional shape isdefined in the X-Y plane.

B6. The system of B0, wherein the root node columns and the child nodecolumns are represented isometrically.

B7. The system of B0, wherein the plurality of instructions are furtherexecutable by the processor to:

represent, adjacent to a first node of the first child nodes, one ormore second child nodes having the first node as a parent, the one ormore second child nodes represented as respective columns extendingsingle file from one unoccupied edge of the first node.

B8. The system of B7, wherein the plurality of instructions are furtherexecutable by the processor to represent, adjacent to a second node ofthe first child nodes, one or more third child nodes having the secondnode as a parent, the one or more third child nodes represented asrespective columns extending single file from one unoccupied edge of thesecond node, such that the third child nodes extend from the samerelative edge of the second node as the second child nodes extend fromthe first node.

B9. The system of B8, wherein the circular, edge-to-edge cluster of rootnode columns defines an X-Y plane, and the second child nodes extendclockwise from the first node and the third child nodes extend clockwisefrom the second node, as viewed from a vantage point normal to the X-Yplane.

B10. The system of B0, wherein the first child nodes each have the samecross-sectional shape as the root node columns.

B11. The system of B0, wherein each of the root node columns isseparated from adjacent root node columns by a gap.

B12. The system of B0, wherein the tessellatable cross-sectional shapeis a hexagon.

B13. The system of B0, wherein receiving the one or more elements of thedata set includes receiving data node relationship information.

B14. The system of B0, wherein the plurality of instructions are furtherexecutable by the processor to display the graphical objectthree-dimensionally in a graphical user interface.

C0. A computer program product for visualizing hierarchical data, thecomputer program product comprising

a non-transitory computer-readable storage medium havingcomputer-readable program code embodied therewith, the computer readableprogram code configured to cause a data processing system to generate agraphical object, the computer readable program code comprising:

at least one instruction to identify a plurality of hierarchical datanodes of a data set, each of the data nodes having an associatedquantitative value, and one or more relationships between the datanodes, such that identifying the data nodes includes identifying aplurality of root nodes and one or more generations of child nodes;

at least one instruction to generate a multi-dimensional graphicalobject illustrating the quantitative values of the data nodes and theone or more relationships between the data nodes, wherein generating thegraphical object includes instructions to:

-   -   represent the plurality of root nodes as a circular,        edge-to-edge cluster of columns, each such root node column        having a tessellatable cross-sectional shape;    -   represent, adjacent to a first root node of the plurality of        root nodes, one or more first child nodes having the first root        node as a parent, the one or more first child nodes represented        as respective child node columns extending single file from one        unoccupied edge of the first root node; and    -   set a respective height of each root node column and of each        child node column, such that the respective height corresponds        to the quantitative value of the data node represented by the        respective column; and

at least one instruction to transmit the graphical object forpresentation on a display.

C1. The computer program product of C0, wherein the graphical object istransmitted for presentation over a data processing network.

C2. The computer program product of C0, wherein the circular,edge-to-edge cluster of root node columns defines an X-Y plane, therespective heights of each root node column being defined along a Z axisrunning orthogonal to the X-Y plane.

C3. The computer program product of C2, wherein the tessellatablecross-sectional shape is defined in the X-Y plane.

C4. The computer program product of C0, wherein the root node columnsand the child node columns are represented isometrically.

C5. The computer program product of C0, the computer readable programcode further comprising at least one instruction to represent, adjacentto a first node of the first child nodes, one or more second child nodeshaving the first node as a parent, the one or more second child nodesrepresented as respective columns extending single file from oneunoccupied edge of the first node.

C6. The computer program product of C5, the computer readable programcode further comprising at least one instruction to represent, adjacentto a second node of the first child nodes, one or more third child nodeshaving the second node as a parent, the one or more third child nodesrepresented as respective columns extending single file from oneunoccupied edge of the second node, such that the third child nodesextend from the same relative edge of the second node as the secondchild nodes extend from the first node.

C7. The computer program product of C6, wherein the circular,edge-to-edge cluster of root node columns defines an X-Y plane, and thesecond child nodes extend clockwise from the first node and the thirdchild nodes extend clockwise from the second node, as viewed from avantage point normal to the X-Y plane.

C8. The computer program product of C0, wherein the first child nodeseach have the same cross-sectional shape as the root node columns.

C9. The computer program product of C0, wherein each of the root nodecolumns is separated from adjacent root node columns by a gap.

C10. The computer program product of C0, wherein the tessellatablecross-sectional shape is a hexagon.

C11. The computer program product of C0, wherein receiving the one ormore elements of the data set includes receiving data node relationshipinformation.

C12. The computer program product of C0, wherein the plurality ofinstructions are further executable by the processor to display thegraphical object three-dimensionally in a graphical user interface.

CONCLUSION

The disclosure set forth above may encompass multiple distinct exampleswith independent utility. Although each of these has been disclosed inits preferred form(s), the specific embodiments thereof as disclosed andillustrated herein are not to be considered in a limiting sense, becausenumerous variations are possible. To the extent that section headingsare used within this disclosure, such headings are for organizationalpurposes only. The subject matter of the invention(s) includes all noveland nonobvious combinations and subcombinations of the various elements,features, functions, and/or properties disclosed herein. The followingclaims particularly point out certain combinations and subcombinationsregarded as novel and nonobvious. Other combinations and subcombinationsof features, functions, elements, and/or properties may be claimed inapplications claiming priority from this or a related application. Suchclaims, whether broader, narrower, equal, or different in scope to theoriginal claims, also are regarded as included within the subject matterof the present disclosure.

What is claimed is:
 1. A method, implemented in a data processingsystem, the method comprising: receiving, using a data processingsystem, one or more elements of a data set; identifying, using aprocessor of the data processing system, a plurality of hierarchicaldata nodes of the data set, each of the data nodes having an associatedfirst quantitative value corresponding to a first time interval and anassociated second quantitative value corresponding to a second timeinterval, and one or more relationships between the data nodes, suchthat identifying the data nodes includes identifying at least one parentnode and one or more generations of child nodes; generating, using thedata processing system, a multi-dimensional graphical objectillustrating the first and second quantitative values of the data nodesand the one or more relationships between the data nodes; whereingenerating the graphical object includes: defining a first referencecylinder having a central axis and a surface; representing the firstquantitative value of a first node of the data nodes as a firstprotruding member extending radially from the surface of the firstreference cylinder at a first axial height and a first angular location,the first protruding member having a radial extent from the surfacecorresponding to the first quantitative value of the first node;representing the second quantitative value of the first node as a secondprotruding member extending radially from the surface of the firstreference cylinder at a second axial height and at the first angularlocation, the second axial height spaced from the first axial heightalong the central axis such that the second protruding member is axiallyadjacent to the first protruding member, the second protruding memberhaving a radial extent from the surface corresponding to the secondquantitative value of the first node; and representing the firstquantitative value of a second node of the data nodes as a thirdprotruding member extending radially from the surface of the firstreference cylinder at the first axial height and at a second angularlocation, the second angular location spaced from the first angularlocation around the central axis, the third protruding member having aradial extent from the surface corresponding to the first quantitativevalue of the second node; and transmitting the graphical object fordisplay.
 2. The method of claim 1, wherein the cylinder is a circularcylinder.
 3. The method of claim 2, wherein each of the protrudingmembers comprises an annular sector.
 4. The method of claim 1, whereinthe first node is a parent node and the second node is a child node ofthe first node.
 5. The method of claim 1, wherein generating thegraphical object further includes: defining a second reference cylinderconcentric with and larger than the first reference cylinder, the secondreference cylinder having a surface and sharing the same central axis asthe first reference cylinder; representing the first quantitative valueof a third node of the data nodes as a third protruding member extendingradially from the surface of the second reference cylinder at the firstaxial height and a third angular location, the third protruding memberhaving a radial extent from the surface corresponding to the firstquantitative value of the third node; and representing the secondquantitative value of the third node as a fourth protruding memberextending radially from the surface of the second reference cylinder atthe second axial height and at the third angular location, such that thefourth protruding member is axially adjacent to the third protrudingmember, the fourth protruding member having a radial extent from thesurface corresponding to the second quantitative value of the thirdnode.
 6. The method of claim 5, wherein the third node is a child nodeof the first node.
 7. The method of claim 6, wherein the firstprotruding member has an angular span around the central axis, and thethird angular location is within the same angular span.
 8. The method ofclaim 1, wherein each of the protruding members extends radially inwardrelative to the central axis if the corresponding quantitative value isless than zero.
 9. A method, implemented in a data processing system,the method comprising: receiving, by a data processing system, a dataset including a first subset of data nodes having first valuesassociated with a first time and second values associated with a secondtime; generating, using the data processing system, a multi-dimensionalgraphical object illustrating the first and second values of the datanodes, wherein generating the graphical object includes: graphicallyrepresenting the first values as coplanar first annular sectorsextending radially from an invisible first cylinder, each first annularsector extending at a same first axial height from a surface of thefirst cylinder, having a respective arc length, and having a respectiveradial length corresponding to a magnitude of the associated firstvalue; and graphically representing the second values as coplanar secondannular sectors extending radially from the first cylinder and axiallyaligned with the first annular sectors, each second annular sectorextending at a same second axial height from the surface of the firstcylinder, having a respective arc length equivalent to the arc length ofthe first annular sector associated with the same data node, and havinga respective radial length corresponding to a magnitude of theassociated second value; such that, with respect to the first cylinder,time is represented axially and magnitude is represented radially. 10.The method of claim 9, wherein the data set further includes a secondsubset of data nodes having third values associated with the first timeand fourth values associated with the second time, the second subset ofdata nodes being in a parent-child relationship with the first subset ofdata nodes; and generating the graphical object further includes:graphically representing the third values as coplanar annular sectorsextending radially from an invisible second cylinder larger than andconcentric with the first cylinder, each annular sector extending at thesame first axial height from a surface of the second cylinder, having arespective arc length, and having a radial length corresponding to amagnitude of the associated third value; and graphically representingthe fourth values as coplanar annular sectors extending radially fromthe second cylinder and axially aligned with the third annular sectors,each annular sector extending at the same second axial height from thesurface of the second cylinder, having a respective arc lengthequivalent to the arc length of the third annular sector associated withthe same data node, and having a respective radial length correspondingto a magnitude of the associated fourth value.
 11. The method of claim10, wherein the first subset of data nodes are parent nodes, and thesecond subset of data nodes comprise child nodes of at least one of theparent nodes.
 12. The method of claim 11, wherein the annular sector ofeach of the child nodes is represented on the second cylinder within anangular span defined by the annular sector of the associated parentnode.
 13. The method of claim 9, wherein the first subset of data nodesincludes a child node and an associated parent node, and wherein thechild node is graphically represented as being circumferentiallyadjacent to the associated parent node.
 14. The method of claim 9,wherein each of the annular sectors is represented as extending from thesurface of the first cylinder toward a central axis if the associatedvalue is negative and away from the central axis if the associated valueis positive.
 15. A data processing system for visualizing hierarchicaldata, the system comprising: a processor; a memory; and a visualizationprogram including a plurality of instructions stored in the memory andexecutable by the processor to: receive one or more elements of a dataset; identify a plurality of hierarchical data nodes of the data set,each of the data nodes having an associated first quantitative valuecorresponding to a first time interval and an associated secondquantitative value corresponding to a second time interval, and one ormore relationships between the data nodes, such that identifying thedata nodes includes identifying at least one parent node and one or moregenerations of child nodes; generate a multi-dimensional graphicalobject illustrating the first and second quantitative values of the datanodes and the one or more relationships between the data nodes, whereingenerating the graphical object includes instructions to: generate afirst cylinder having a long axis and a first radius defining a surfaceof the first cylinder, the surface having a circumference; representeach first quantitative value of a selected first subset of the datanodes as a respective first annular sector, such that the first annularsectors are arranged in coplanar fashion around the circumference of thefirst cylinder, each of the first annular sectors having a respectivearc length, originating at a first axial height on the surface of thefirst cylinder, and extending radially, a respective radial length ofeach first annular sector corresponding to a magnitude of the associatedfirst quantitative value; and represent each second quantitative valueof the first subset of the data nodes as a respective second annularsector, such that the second annular sectors are axially aligned withthe first annular sectors and arranged in coplanar fashion around thecircumference of the first cylinder, each of the second annular sectorshaving the same respective arc length as the corresponding first annularsector, originating at a second axial height on the surface of the firstcylinder, and extending radially, a respective radial length of eachsecond annular sector corresponding to a magnitude of the associatedsecond quantitative value; such that, with respect to the firstcylinder, time is represented axially and magnitude is representedradially; and transmitting the graphical object for display.
 16. Themethod of claim 15, wherein the first cylinder is invisible.
 17. Themethod of claim 15, wherein each annular sector associated with anegative quantitative value extends radially inward with respect to thefirst cylinder.
 18. The method of claim 15, wherein generating thegraphical object further includes instructions to: generate a secondcylinder coaxial with the first cylinder and having a second radiusdefining a surface of the second cylinder, the surface having acircumference, such that the second radius is greater than the firstradius and the first and second cylinders are concentric; represent eachfirst quantitative value of a selected second subset of the data nodesas a respective third annular sector, such that the third annularsectors are arranged in coplanar fashion around the circumference of thesecond cylinder, each of the third annular sectors having a respectivearc length, originating at the first axial height on the surface of thesecond cylinder, and extending radially, a respective radial length ofeach third annular sector corresponding to a magnitude of the associatedfirst quantitative value; and representing each second quantitativevalue of the second subset of the data nodes as a respective fourthannular sector, such that the fourth annular sectors are axially alignedwith the third annular sectors and arranged in coplanar fashion aroundthe circumference of the second cylinder, each of the second annularsectors having the same respective arc length as the corresponding thirdannular sector, originating at the second axial height on the surface ofthe second cylinder, and extending radially, a respective radial lengthof each fourth annular sector corresponding to a magnitude of theassociated second quantitative value; wherein the second subset of datanodes are hierarchically related to the first subset of data nodes, andthe relationship is indicated by representing related nodes atcoinciding radial positions on the first and second cylinders.
 19. Themethod of claim 18, wherein the first subset of data nodes are parentnodes, and the second subset of data nodes are a first generation ofchild nodes with respect to at least one of the parent nodes.
 20. Themethod of claim 15, wherein the first subset of data nodes includes atleast one parent node and a first generation of child nodes, the firstannular sectors of the at least one parent node and the first generationof child nodes being represented such that a first of the child nodes isadjacent to the parent node and remaining child nodes continue in radialadjacency around the circumference of the first cylinder.